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{"sheet":"Topics","index":0,"n_rows":11,"n_cols":1,"rows_kept":11,"cut":false,"hidden":false,"merged":[]}
["Continuous Probability Distribution"]
["Uniform Probability Distribution"]
["Normal Probability Distribution"]
["Standard Normal Probability Distribution"]
["NORM.DIST Excel function"]
["NORM.INV Excel function"]
["NORM.S.DIST Excel function"]
["NORM.S.INV Excel function"]
["Exponential Probability Distribution"]
["EXPON.DIST Excel function"]
["Relationship between Poisson and Exponential Probability Distributions"]

{"sheet":"B","index":1,"n_rows":88,"n_cols":4,"rows_kept":88,"cut":false,"hidden":false,"merged":[]}
["n",10,null,{"$f":"\"Binomial Distribution, n = \"&B1&\" p = \"&B2&\" \"&C8","v":"Binomial Distribution, n = 10 p = 0.5 P(X<=4)"}]
["p",0.5,null,{"$f":"C8&\" = \"&TEXT(B6,\"0.0000\")","v":"P(X<=4) = 0.3770"}]
["X",4]
["Comparative Operator","<="]
["Result",{"$f":"B4&B3","v":"<=4"}]
["BINOMDIST",{"$f":"_xlfn.BINOM.DIST(B3,B1,B2,1)","v":0.376953125}]
[]
["X","p(x)",{"$f":"\"P(X\"&B5&\")\"","v":"P(X<=4)"}]
[0,{"$f":"_xlfn.BINOM.DIST(A9,$B$1,$B$2,0)","v":9.765625E-4},{"$f":"IF(A9<=$B$3,B9,\"\")","v":9.765625E-4}]
[1,{"$f":"_xlfn.BINOM.DIST(A10,$B$1,$B$2,0)","v":9.7656250000000017E-3},{"$f":"IF(A10<=$B$3,B10,\"\")","v":9.7656250000000017E-3}]
[2,4.3945312499999972E-2,4.3945312499999972E-2]
[3,0.11718750000000003,0.11718750000000003]
[4,0.20507812500000006,0.20507812500000006]
[5,0.24609375000000008,""]
[6,0.20507812500000006,""]
[7,0.11718750000000003,""]
[8,4.3945312499999986E-2,""]
[9,9.7656250000000017E-3,""]
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{"sheet":"CPD Notes","index":2,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Uniform(1)","index":3,"n_rows":34,"n_cols":4,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
[null,null,"Test Score Category","Frequency"]
[0,10,{"$f":"A2&\" up to \"&B2","v":"0 up to 10"},1]
[{"$f":"B2","v":10},{"$f":"B2+10","v":20},"10 up to 20",2]
[{"$f":"B3","v":20},30,"20 up to 30",3]
[30,40,"30 up to 40",10]
[40,50,"40 up to 50",12]
[50,60,"50 up to 60",15]
[{"$f":"B7","v":60},70,"60 up to 70",18]
[70,80,"70 up to 80",22]
[80,90,"80 up to 90",15]
[{"$f":"B10","v":90},100,"90 up to 100",2]
[null,null,null,{"$f":"SUM(D2:D11)","v":100}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,"Test Score Category","Frequency"]
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[{"$f":"B24","v":10},{"$f":"B24+10","v":20},"10 up to 20",10]
[{"$f":"B25","v":20},30,"20 up to 30",10]
[30,40,"30 up to 40",10]
[40,50,"40 up to 50",10]
[50,60,"50 up to 60",10]
[{"$f":"B29","v":60},70,"60 up to 70",10]
[70,80,"70 up to 80",10]
[80,90,"80 up to 90",10]
[{"$f":"B32","v":90},100,"90 up to 100",10]
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{"sheet":"Uniform(2)","index":4,"n_rows":19,"n_cols":12,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
["Driving Distance for the top 100 golfers on the PGA tour (2003)",null,null,"f(x) = height"]
["Distribution is Uniform",null,null,{"$f":"1/(B4-B3)","v":3.8610038610038561E-2}]
["Lower",284.7,"yards"]
["Upper",310.60000000000002,"yards"]
["Difference = width",{"$f":"B4-B3","v":25.900000000000034},"yards"]
[null,null,null,null,{"$f":"B3","v":284.7},null,null,null,null,{"$f":"B4","v":310.60000000000002},null,"x"]
["Probability Density function of driving distances:",null,null,null,null,{"$f":"\"b - a = width = \"&J6&\" - \"&E6&\" = \"&J6-E6","v":"b - a = width = 310.6 - 284.7 = 25.9"}]
[{"$f":"IF(AND(B3:B4=\"\"),\"\",\"F(x) = 1/(\"&B4&\"-\"&B3&\")\"&\" = 1/\"&B4-B3&CHAR(10)&\"for interval \"&B3&\" <= x <= \"&B4&\" and 0 elsewhere.\")","v":"F(x) = 1/(310.6-284.7) = 1/25.9\nfor interval 284.7 <= x <= 310.6 and 0 elsewhere."}]
["height =  f(x) = 1/(b-a)",{"$f":"1/(B4-B3)","v":3.8610038610038561E-2},null,null,null,"Formulas:"]
[null,null,null,null,null,"Area = Probability"]
[null,null,null,null,null,"All probability = 1"]
[null,null,null,null,null,"Area = width * height"]
[null,null,null,null,null,"1 = width * height"]
[null,null,null,null,null,"height = 1/width"]
[null,null,null,null,null,"height = Probability Density function = f(x) = 1/(b-a)"]
[null,null,null,null,null,"P(x1<=x<=x2 ) = (x2-x1)*1/(b-a)"]
[null,null,null,null,null,"P(x1<=x<=x2 ) = P(x1<x<x2 ) because lines have no area"]
[null,null,null,null,null,"Mean = (a+ b)/2"]
[null,null,null,null,null,"SD = SQRT((b-a)^2/12)"]

{"sheet":"Uniform (3)","index":5,"n_rows":30,"n_cols":12,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["Driving Distance for the top 100 golfers on the PGA tour (2003)"]
["Distribution is Uniform"]
["Lower",284.7,"yards"]
["Upper",310.60000000000002,"yards"]
["Difference = width",null,"yards"]
[]
["Probability Density function of driving distances:"]
[{"$f":"IF(AND(B3:B4=\"\"),\"\",\"F(x) = 1/(\"&B4&\"-\"&B3&\")\"&\" = 1/\"&B4-B3&CHAR(10)&\"for interval \"&B3&\" <= x <= \"&B4&\" and 0 elsewhere.\")","v":"F(x) = 1/(310.6-284.7) = 1/25.9\nfor interval 284.7 <= x <= 310.6 and 0 elsewhere."}]
["height =  f(x) = 1/(b-a)"]
[]
["What is probability of one of the golfers driving less than 290 yards?",null,null,"f(x) = height"]
["X1",{"$f":"B3","v":284.7},null,{"$f":"1/(B4-B3)","v":3.8610038610038561E-2}]
["X2",290]
["area = width * height = (X2-X1)*1/(b-a) ="]
[{"$f":"\"P(X<\"&B13&\") = (\"&B13&\" - \"&B12&\")*1/(\"&$B$4&\" - \"&$B$3&\")\"","v":"P(X<290) = (290 - 284.7)*1/(310.6 - 284.7)"}]
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[]
["What is probability of one of the golfers driving more than 290 yards?",null,null,"f(x) = height"]
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["X2",{"$f":"B4","v":310.60000000000002}]
["area = width * height = (X2-X1)*1/(b-a) ="]
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[]
["What is probability of one of the golfers driving between 290 and 300?",null,null,"f(x) = height"]
["X1",290,null,{"$f":"D19","v":3.8610038610038561E-2}]
["X2",300]
["area = width * height = (X2-X1)*1/(b-a) ="]
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["Driving Distance for the top 100 golfers on the PGA tour (2003)"]
["Distribution is Uniform"]
["Lower",284.7,"yards",null,"f(x)"]
["Upper",310.60000000000002,"yards",null,"1/25.9"]
["Difference = width",{"$f":"B4-B3","v":25.900000000000034},"yards"]
[]
["Probability Density function of driving distances:"]
[{"$f":"IF(AND(B3:B4=\"\"),\"\",\"F(x) = 1/(\"&B4&\"-\"&B3&\")\"&\" = 1/\"&B4-B3&CHAR(10)&\"for interval \"&B3&\" <= x <= \"&B4&\" and 0 elsewhere.\")","v":"F(x) = 1/(310.6-284.7) = 1/25.9\nfor interval 284.7 <= x <= 310.6 and 0 elsewhere."},null,null,null,null,null,{"$f":"B3","v":284.7},290,null,{"$f":"B4","v":310.60000000000002},null,"x"]
["height =  f(x) = 1/(b-a)",{"$f":"1/B5","v":3.8610038610038561E-2}]
[]
["What is probability of one of the golfers driving less than 290 yards?",null,null,"f(x) = height"]
["X1",{"$f":"B3","v":284.7},null,{"$f":"1/(B4-B3)","v":3.8610038610038561E-2}]
["X2",290]
["area = width * height = (X2-X1)*1/(b-a) =",{"$f":"(B13-B12)*B9","v":0.20463320463320481}]
[{"$f":"\"P(X<\"&B13&\") = (\"&B13&\" - \"&B12&\")*1/(\"&$B$4&\" - \"&$B$3&\")\"","v":"P(X<290) = (290 - 284.7)*1/(310.6 - 284.7)"}]
[null,null,null,null,{"$f":"B3","v":284.7},null,{"$f":"B13","v":290},null,null,{"$f":"B4","v":310.60000000000002},null,"x"]
[]
["What is probability of one of the golfers driving more than 290 yards?",null,null,"f(x) = height"]
["X1",290,null,{"$f":"D12","v":3.8610038610038561E-2}]
["X2",{"$f":"B4","v":310.60000000000002}]
["area = width * height = (X2-X1)*1/(b-a) =",{"$f":"(B20-B19)*$B$9","v":0.79536679536679522}]
[{"$f":"\"P(X>\"&B20&\") = (\"&B20&\" - \"&B19&\")*1/(\"&$B$4&\" - \"&$B$3&\")\"","v":"P(X>310.6) = (310.6 - 290)*1/(310.6 - 284.7)"}]
[null,null,null,null,{"$f":"$E$16","v":284.7},null,{"$f":"$G$16","v":290},null,null,{"$f":"$J$16","v":310.60000000000002},null,"x"]
[]
["What is probability of one of the golfers driving between 290 and 300?",null,null,"f(x) = height"]
["X1",290,null,{"$f":"D19","v":3.8610038610038561E-2}]
["X2",300]
["area = width * height = (X2-X1)*1/(b-a) =",{"$f":"(B27-B26)*$B$9","v":0.38610038610038561}]
[{"$f":"\"P(X>\"&B27&\") = (\"&B27&\" - \"&B26&\")*1/(\"&$B$4&\" - \"&$B$3&\")\"","v":"P(X>300) = (300 - 290)*1/(310.6 - 284.7)"}]
[null,null,null,null,{"$f":"$E$16","v":284.7},null,{"$f":"$G$16","v":290},null,300,null,null,"x"]

{"sheet":"PSQS","index":7,"n_rows":242,"n_cols":29,"rows_kept":242,"cut":false,"hidden":false,"merged":[]}
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[12,null,"SD = sigma =",{"$f":"ROUND(STDEVP(A2:A166),0)","v":2},null,null,{"$f":"(ROWS(H$2:H5)-1)&\" up to \"&ROWS(H$2:H5)","v":"3 up to 4"},4,0,0,0,5.5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.3,0]
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[17,null,null,{"$f":"C1&\" = \"&D1","v":"Mean = mu = = 12"},null,null,{"$f":"(ROWS(H$2:H7)-1)&\" up to \"&ROWS(H$2:H7)","v":"5 up to 6"},6,1,6.0606060606060606E-3,0,7.5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.5,0]
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[11,null,null,{"$f":"C4&\" = \"&D4","v":"Skew = 0"},null,null,{"$f":"(ROWS(H$2:H10)-1)&\" up to \"&ROWS(H$2:H10)","v":"8 up to 9"},9,14,8.4848484848484854E-2,1.8181818181818181E-2,10.5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.8,0]
[12,null,null,{"$f":"C5&\" = \"&D5","v":"SD = sigma = = 2"},null,null,{"$f":"(ROWS(H$2:H11)-1)&\" up to \"&ROWS(H$2:H11)","v":"9 up to 10"},10,18,0.10909090909090909,8.4848484848484854E-2,11.5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.9,0]
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{"sheet":"N Notes","index":8,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Normal","index":9,"n_rows":4084,"n_cols":11,"rows_kept":4084,"cut":false,"hidden":false,"merged":[]}
["x = Test Scores",13,null,null,null,null,null,"X","z","Height",{"$f":"\"X<\"&B1","v":"X<13"}]
["mean = μ",12,null,null,null,null,null,{"$f":"I2*$B$3+$B$2","v":7},-5,{"$f":"_xlfn.NORM.DIST(H2,$B$2,$B$3,0)","v":1.4867195147342977E-6},{"$f":"IF(H2<$B$1,J2,\"\")","v":1.4867195147342977E-6}]
["SD = σ",1,null,null,null,null,null,7.1,{"$f":"I2+0.1","v":-4.9000000000000004},{"$f":"_xlfn.NORM.DIST(H3,$B$2,$B$3,0)","v":2.4389607458933522E-6},2.4389607458933522E-6]
[{"$f":"A2&\" = \"&B2&\". \"&A3&\" = \"&B3&\".\"","v":"mean = μ = 12. SD = σ = 1."},null,null,null,null,null,null,7.1999999999999993,-4.8000000000000007,3.9612990910320609E-6,3.9612990910320609E-6]
["# SD",5,null,null,null,null,null,7.2999999999999989,-4.7000000000000011,6.3698251788670679E-6,6.3698251788670679E-6]
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{"sheet":"SNormal","index":10,"n_rows":102,"n_cols":9,"rows_kept":102,"cut":false,"hidden":false,"merged":[]}
["x = Test Scores",10,"X","z","Height",{"$f":"\"X<\"&B1","v":"X<10"}]
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["SD = σ",2,2.1999999999999993,{"$f":"D2+0.1","v":-4.9000000000000004},{"$f":"_xlfn.NORM.DIST(C3,$B$2,$B$3,0)","v":1.2194803729466761E-6},1.2194803729466761E-6]
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[null,null,2.7999999999999972,-4.6000000000000014,5.0704260327433351E-6,5.0704260327433351E-6]
[null,null,2.9999999999999964,-4.5000000000000018,7.9918705534526814E-6,7.9918705534526814E-6]
[null,null,3.1999999999999957,-4.4000000000000021,1.2471235645026678E-5,1.2471235645026678E-5]
[null,null,3.399999999999995,-4.3000000000000025,1.9267598371043358E-5,1.9267598371043358E-5]
[null,null,3.5999999999999943,-4.2000000000000028,2.9471533878269558E-5,2.9471533878269558E-5,null,null,"x = actual test score"]
[null,null,3.7999999999999936,-4.1000000000000032,4.4630828588565827E-5,4.4630828588565827E-5]
[null,null,3.9999999999999929,-4.0000000000000036,6.6915112882441735E-5,6.6915112882441735E-5,null,null,"z = Standard Normal Random Variable = # of"]
[null,null,4.1999999999999931,-3.9000000000000035,9.9327735696384949E-5,9.9327735696384949E-5,null,null,"standard Deviations away from mean"]
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{"sheet":"<= Prob","index":11,"n_rows":260,"n_cols":11,"rows_kept":260,"cut":false,"hidden":false,"merged":[[15,1,22,1],[23,1,28,1],[19,9,24,12]]}
["Because we have looked at past data for test scores for a particular instructor and have seen that the distribution (histogram chart) is approximately bell shaped, we can use the bell curve to estimate probabilities"]
["In chapter 6, we know population mean and standard deviation (mew and sigma). Later we will see how to do similar calculations for sample data (after we learn Central Limit Theorem)."]
["Based on past data, estimate the percentage of scores on the next statistics test that will be 10 points or less."]
["Test Score","x",10]
[null,"Operator 1","<="]
[null,"Operator 2"]
[null,"mean = mew = μ =",12]
[null,"standard deviation = sigma = σ =",2]
[null,"Z",null,null,"Sum of Heights","old functions"]
[null,{"$f":"\"p(X \"&$C$5&\" \"&C4&\")\"","v":"p(X <= 10)"}]
[null,{"$f":"\"p(Z \"&C5&\" \"&C9&\")\"","v":"p(Z <= )"},null,null,"**Not allowed"]
[null,"What is x given cumulative Probability?"]
[null,"What is z given cumulative Probability?"]
[0.1,{"$f":"\"What score do you need to be in to be top \"&TEXT(A14,\"0%\")&\"?\"","v":"What score do you need to be in to be top 10%?"}]
[null,"P(X>=10)",null,null,"Where should we start?",null,"x = low",{"$f":"C7-C8*6","v":0},null,0.99," + / - 3 SD"]
[null,{"$f":"IF(C10<>\"\",\"Based on past data it would be reasonable to assume that on the next test there is a \"&TEXT(C10,\"0.00%\")&\" chance that a score selected at random would be \"&C4&\" or less, or that \"&TEXT(C10,\"0.00%\")&\" of all the scores on the next test will be \"&C4&\" or less.\",\"\")","v":""},null,null,"Where should we end?",null,"x = high",{"$f":"C7+C8*6","v":24}]
[null,null,null,null,"Chart Label",{"$f":"\"Test Scores with a mew of \"&C7&\", and sigma of \"&C8","v":"Test Scores with a mew of 12, and sigma of 2"}]
[null,null,null,null,null,null,"Height of curve"]
[null,null,null,null,"z",{"$f":"B4&\" = \"&A4","v":"x = Test Score"},{"$f":"B15&\" = \"&ROUND(C15,4)","v":"P(X>=10) = 0"},{"$f":"\"P(x<=\"&C4&\") = \"&ROUND(C10,4)","v":"P(x<=10) = 0"}]
[null,null,null,null,{"$f":"(F20-$C$7)/$C$8","v":-6},0,{"$f":"_xlfn.NORM.DIST(F20,$C$7,$C$8,0)","v":3.037941424911643E-9},{"$f":"IF(F20<=$C$4,G20,\"\")","v":3.037941424911643E-9},null,"F17 has the formula:\n=NORM.DIST(E20,$C$7,$C$8,0)\nG17 has the formula:\n=IF(E20<=$C$4,F20,\"\")"]
[null,null,null,null,{"$f":"(F21-$C$7)/$C$8","v":-5.95},0.1,{"$f":"_xlfn.NORM.DIST(F21,$C$7,$C$8,0)","v":4.0956692017395868E-9},{"$f":"IF(F21<=$C$4,G21,\"\")","v":4.0956692017395868E-9}]
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[null,null,null,null,-5.85,0.30000000000000004,7.3885397932400267E-9,7.3885397932400267E-9]
[null,{"$f":"\"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(\"&C5&C4&\") = P(\"&LEFT(C5,1)&C4&\")\"","v":"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(<=10) = P(<10)"},null,null,-5.8,0.4,9.8865982031223359E-9,9.8865982031223359E-9]
[null,null,null,null,-5.75,0.5,1.3196216017852868E-8,1.3196216017852868E-8]
[null,null,null,null,-5.7,0.60000000000000009,1.756977547410217E-8,1.756977547410217E-8]
[null,null,null,null,-5.65,0.70000000000000007,2.333443398797128E-8,2.333443398797128E-8,null,"Chart Steps:"]
[null,null,null,null,-5.6,0.8,3.0913102500829286E-8,3.0913102500829286E-8,null,"Create Chart Label in cell F17: =\"Bell Curve For Test Scores, mew = \"&C7&\", sigma = \"&C8"]
[null,null,null,null,-5.55,0.9,4.0850951892716102E-8,4.0850951892716102E-8,null,"Create series label in cell G19: =\"Remaining Area = \"&ROUND(1-C10,4)"]
[null,null,null,null,-5.5,1,5.384880021271638E-8,5.384880021271638E-8,null,"Create series label in cell H19: =\"P(x<=\"&C4&\") = \"&ROUND(C10,4)"]
[null,null,null,null,-5.45,1.1000000000000001,7.0805035650805879E-8,7.0805035650805879E-8,null,"Create x values (type 0, right-click fill handle, Series, Columns, Step .01, End = 24, Ok)"]
[null,null,null,null,-5.4,1.2000000000000002,9.2868092227764484E-8,9.2868092227764484E-8,null,"Create z values"]
[null,null,null,null,-5.35,1.3,1.2150192705402675E-7,1.2150192705402675E-7,null,"Plot Height Values with Area Chart"]
[null,null,null,null,-5.3,1.4000000000000001,1.585674608357988E-7,1.585674608357988E-7,null,"Edit horizontal Axis (ChartTools Design tab Ribbon, Select Data button)"]
[null,null,null,null,-5.25,1.5,2.0642354943149992E-7,2.0642354943149992E-7,null,"Plot Secondary Heights"]
[null,null,null,null,-5.2,1.6,2.6805176723488073E-7,2.6805176723488073E-7,null,"Right-click secondary Heights on chart and Ctrl + 1 to open Format Chart Element dialog box, change series to secondary axis."]
[null,null,null,null,-5.15,1.7000000000000002,3.4721011769276696E-7,3.4721011769276696E-7,null,"Delete Vertical Axis on right"]
[null,null,null,null,-5.0999999999999996,1.8,4.4862175811916687E-7,4.4862175811916687E-7,null,"ChartTools Layout tab Ribbon, \"Axes\" button in Axes group, Secondary Horizontal Axis, Show Left to Right Axis"]
[null,null,null,null,-5.05,1.9000000000000001,5.782059517898917E-7,5.782059517898917E-7,null,"Click on Axis, Ctrl + 1, Axis Options, Axis Labels = Low"]
[null,null,null,null,-5,2,7.4335975736714884E-7,7.4335975736714884E-7,null,"Move Legend"]
[null,null,null,null,-4.95,2.1,9.5330045156140538E-7,9.5330045156140538E-7,null,"Add Chart Title linked to cell"]
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[null,null,null,null,-4.6500000000000004,2.7,4.0235912282461476E-6,4.0235912282461476E-6]
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["Because we have looked at past data for test scores for a particuklar instructor and have seen that the distribution (histogram chart) is aproximately bell shaped, we can use the bell curve to esimate probabilities"]
["In chapter 6, we know population mean and standard deviation (mew and sigma). Later we will see how to do similar calculations for sample data (after we learn Central Limit Theorem)."]
["Based on past data, estimate the percentage of scores on the next statistics test that will be 10 or less."]
["Test Score","x",10]
[null,"Operator 1","<="]
[null,"Operator 2"]
[null,"mean = mu = μ =",12]
[null,"standard deviation = sigma = σ =",2]
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[null,"What is x given cumulative Probability?",{"$f":"_xlfn.NORM.INV(C10,C7,C8)","v":10},null,null,{"$f":"NORMINV(C10,C7,C8)","v":10},{"$f":"F12=C12","v":true}]
[null,"What is z given cumulative Probability?",{"$f":"_xlfn.NORM.S.INV(C11)","v":-0.99999999999999956},null,null,{"$f":"NORMSINV(C11)","v":-0.99999999999999956},{"$f":"F13=C13","v":true}]
[0.1,{"$f":"\"What score do you have to be in to be top \"&TEXT(A14,\"0%\")&\"?\"","v":"What score do you have to be in to be top 10%?"},{"$f":"_xlfn.NORM.INV(1-A14,C7,C8)","v":14.563103131089202}]
[null,"remaining area",{"$f":"1-C10","v":0.84134474606854304},null,"Where should we start?",null,"x =",{"$f":"$C$7-$C$8*6","v":0}]
[null,{"$f":"IF(C10<>\"\",\"Based on past data it would be reasonable to assume that on the next test there is a \"&TEXT(C10,\"0.00%\")&\" chance that a score selected at random would be \"&C4&\" or less, or that \"&TEXT(C10,\"0.00%\")&\" of all the scores on the next test will be \"&C4&\" or less.\",\"\")","v":"Based on past data it would be reasonable to assume that on the next test there is a 15.87% chance that a score selected at random would be 10 or less, or that 15.87% of all the scores on the next test will be 10 or less."},null,null,"Where should we end?",null,"x =",{"$f":"$C$7+$C$8*6","v":24}]
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[null,null,null,null,3.6000000000000014,19.200000000000003,3.0595096505688459E-4,""]
[null,null,null,null,{"$f":"(F213-$C$7)/$C$8","v":3.6500000000000004},19.3,{"$f":"_xlfn.NORM.DIST(F213,$C$7,$C$8,0)","v":2.5523248717209237E-4},{"$f":"IF(F213<=$C$4,G213,\"\")","v":""}]
[null,null,null,null,3.7000000000000011,19.400000000000002,2.1239013527537499E-4,""]
[null,null,null,null,3.75,19.5,1.762978411837227E-4,""]
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[null,"Total is not 1 because not Probability",null,null,4.1000000000000014,20.200000000000003,4.4630828588566152E-5,""]
[null,null,null,null,4.1500000000000004,20.3,3.6312965151126162E-5,""]
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{"sheet":"<= Chart","index":13,"n_rows":222,"n_cols":11,"rows_kept":222,"cut":false,"hidden":false,"merged":[[15,1,22,1],[19,9,24,12],[23,1,28,1]]}
["Because we have looked at past data for test scores for a particular instructor and have seen that the distribution (histogram chart) is approximately bell shaped, we can use the bell curve to estimate probabilities"]
["In chapter 6, we know population mean and standard deviation (mew and sigma). Later we will see how to do similar calculations for sample data (after we learn Central Limit Theorem)."]
["Based on past data, estimate the percentage of scores on the next statistics test that will be 10 points or less."]
["Test Score","x",10]
[null,"Operator 1","<="]
[null,"Operator 2"]
[null,"mean = mew = μ =",12]
[null,"standard deviation = sigma = σ =",2]
[null,"Z",{"$f":"(C4-C7)/C8","v":-1},null,"Sum of Heights","old functions"]
[null,{"$f":"\"P(X \"&$C$5&\" \"&C4&\")\"","v":"P(X <= 10)"},{"$f":"_xlfn.NORM.DIST(C4,C7,C8,1)","v":0.15865525393145699},null,null,{"$f":"NORMDIST(C4,C7,C8,1)","v":0.15865525393145699},{"$f":"F10=C10","v":true}]
[null,{"$f":"\"p(Z \"&C5&\" \"&C9&\")\"","v":"p(Z <= -1)"},{"$f":"_xlfn.NORM.S.DIST(C9,1)","v":0.15865525393145699},null,"**Not allowed",{"$f":"NORMSDIST(C9)","v":0.15865525393145699},{"$f":"F11=C11","v":true}]
[null,"What is x given cumulative Probability?",{"$f":"_xlfn.NORM.INV(1-A14,C7,C8)","v":14.563103131089202},null,null,{"$f":"NORMINV(1-A14,C7,C8)","v":14.563103131089202},{"$f":"F12=C12","v":true}]
[null,"What is z given cumulative Probability?",{"$f":"_xlfn.NORM.S.INV(1-A14)","v":1.2815515655446006},null,null,{"$f":"NORMSINV(1-A14)","v":1.2815515655446006},{"$f":"F13=C13","v":true}]
[0.1,{"$f":"\"What score do you need to be in to be top \"&TEXT(A14,\"0%\")&\"?\"","v":"What score do you need to be in to be top 10%?"},{"$f":"C7+C8*C13","v":14.563103131089202},null,"Test Score sigma",2,"Test Score mew",{"$f":"C7","v":12}]
[null,{"$f":"\"P(X >= \"&C4&\")\"","v":"P(X >= 10)"},{"$f":"1-C10","v":0.84134474606854304},null,"Where should we start?",null,"x = low",null,null,0.99," + / - 3 SD"]
[null,{"$f":"IF(C10<>\"\",\"Based on past data it would be reasonable to assume that on the next test there is a \"&TEXT(C10,\"0.00%\")&\" chance that a score selected at random would be \"&C4&\" or less, or that \"&TEXT(C10,\"0.00%\")&\" of all the scores on the next test will be \"&C4&\" or less.\",\"\")","v":"Based on past data it would be reasonable to assume that on the next test there is a 15.87% chance that a score selected at random would be 10 or less, or that 15.87% of all the scores on the next test will be 10 or less."},null,null,"Where should we end?",null,"x = high"]
[null,null,null,null,"Chart Label",{"$f":"\"Bell Curve For Test Scores With Mew = \"&H14&\" And Sigma = \"&F14","v":"Bell Curve For Test Scores With Mew = 12 And Sigma = 2"}]
[null,null,null,null,null,null,"Height of curve"]
[null,null,null,null,"z",{"$f":"B4&\" = \"&A4","v":"x = Test Score"},{"$f":"\"P(x>=\"&C4&\") = \"&ROUND(C15,4)","v":"P(x>=10) = 0.8413"},{"$f":"\"P(x<=\"&C4&\") = \"&ROUND(C10,4)","v":"P(x<=10) = 0.1587"}]
[null,null,null,null,null,null,null,null,null,"F17 has the formula:\n=NORM.DIST(E20,$C$7,$C$8,0)\nG17 has the formula:\n=IF(E20<=$C$4,F20,\"\")"]
[]
[]
[]
[null,{"$f":"\"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(\"&C5&C4&\") = P(\"&LEFT(C5,1)&C4&\")\"","v":"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(<=10) = P(<10)"}]
[]
[]
[null,null,null,null,null,null,null,null,null,"Chart Steps:"]
[null,null,null,null,null,null,null,null,null,"Create Chart Label in cell F17: =\"Bell Curve For Test Scores, mew = \"&C7&\", sigma = \"&C8"]
[null,null,null,null,null,null,null,null,null,"Create series label in cell G19: =\"Remaining Area = \"&ROUND(1-C10,4)"]
[null,null,null,null,null,null,null,null,null,"Create series label in cell H19: =\"P(x<=\"&C4&\") = \"&ROUND(C10,4)"]
[null,null,null,null,null,null,null,null,null,"Create x values (type 0, right-click fill handle, Series, Columns, Step .01, End = 24, Ok)"]
[null,null,null,null,null,null,null,null,null,"Create z values"]
[null,null,null,null,null,null,null,null,null,"Plot Height Values with Area Chart"]
[null,null,null,null,null,null,null,null,null,"Edit horizontal Axis (ChartTools Design tab Ribbon, Select Data button)"]
[null,null,null,null,null,null,null,null,null,"Plot Secondary Heights"]
[null,null,null,null,null,null,null,null,null,"Right-click secondary Heights on chart and Ctrl + 1 to open Format Chart Element dialog box, change series to secondary axis."]
[null,null,null,null,null,null,null,null,null,"Delete Vertical Axis on right"]
[null,null,null,null,null,null,null,null,null,"ChartTools Layout tab Ribbon, \"Axes\" button in Axes group, Secondary Horizontal Axis, Show Left to Right Axis"]
[null,null,null,null,null,null,null,null,null,"Click on Axis, Ctrl + 1, Axis Options, Axis Labels = Low"]
[null,null,null,null,null,null,null,null,null,"Move Legend"]
[null,null,null,null,null,null,null,null,null,"Add Chart Title linked to cell"]
[]
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[null,"Total is not 1 because not Probability"]

{"sheet":"<= Prob Chart (an)","index":14,"n_rows":260,"n_cols":10,"rows_kept":260,"cut":false,"hidden":false,"merged":[[15,1,22,1],[19,9,24,12],[23,1,28,1]]}
["Because we have looked at past data for test scores for a particular instructor and have seen that the distribution (histogram chart) is approximately bell shaped, we can use the bell curve to estimate probabilities"]
["In chapter 6, we know population mean and standard deviation (mew and sigma). Later we will see how to do similar calculations for sample data (after we learn Central Limit Theorem)."]
["Based on past data, estimate the percentage of scores on the next statistics test that will be 10 points or less."]
["Test Score","x",14]
[null,"Operator 1","<="]
[null,"Operator 2"]
[null,"mean = mew = μ =",12,null,null,0.99," + / - 3 SD"]
[null,"standard deviation = sigma = σ =",2]
[null,"Z",{"$f":"(C4-C7)/C8","v":1},null,"Sum of Heights","old functions"]
[null,{"$f":"\"p(X \"&$C$5&\" \"&C4&\")\"","v":"p(X <= 14)"},{"$f":"_xlfn.NORM.DIST(C4,C7,C8,1)","v":0.84134474606854304},null,{"$f":"SUM(G20:G160)","v":8.4734359857000747},{"$f":"NORMDIST(C4,C7,C8,1)","v":0.84134474606854304},{"$f":"F10=C10","v":true}]
[null,{"$f":"\"p(Z \"&C5&\" \"&C9&\")\"","v":"p(Z <= 1)"},{"$f":"_xlfn.NORM.S.DIST(C9,1)","v":0.84134474606854304},null,"**Not allowed",{"$f":"NORMSDIST(C9)","v":0.84134474606854304},{"$f":"F11=C11","v":true}]
[null,"What is x given cumulative Probability?",{"$f":"_xlfn.NORM.INV(1-A14,C7,C8)","v":14.563103131089202},null,null,{"$f":"NORMINV(1-A14,C7,C8)","v":14.563103131089202},{"$f":"F12=C12","v":true}]
[null,"What is z given cumulative Probability?",{"$f":"_xlfn.NORM.S.INV(1-A14)","v":1.2815515655446006},null,null,{"$f":"NORMSINV(1-A14)","v":1.2815515655446006},{"$f":"F13=C13","v":true}]
[0.1,{"$f":"\"What score do you need to be in to be top \"&TEXT(A14,\"0%\")&\"?\"","v":"What score do you need to be in to be top 10%?"},{"$f":"C7+C8*C13","v":14.563103131089202}]
[null,"P(X>=10)",{"$f":"1-C10","v":0.15865525393145696},null,"Where should we start?",null,"x = low",{"$f":"C7-C8*6","v":0}]
[null,{"$f":"IF(C10<>\"\",\"Based on past data it would be reasonable to assume that on the next test there is a \"&TEXT(C10,\"0.00%\")&\" chance that a score selected at random would be \"&C4&\" or less, or that \"&TEXT(C10,\"0.00%\")&\" of all the scores on the next test will be \"&C4&\" or less.\",\"\")","v":"Based on past data it would be reasonable to assume that on the next test there is a 84.13% chance that a score selected at random would be 14 or less, or that 84.13% of all the scores on the next test will be 14 or less."},null,null,"Where should we end?",null,"x = high",{"$f":"C7+C8*6","v":24}]
[null,null,null,null,"Chart Label",{"$f":"\"Test Scores with a mew of \"&C7&\", and sigma of \"&C8","v":"Test Scores with a mew of 12, and sigma of 2"}]
[null,null,null,null,null,null,"Height of curve"]
[null,null,null,null,"z",{"$f":"B4&\" = \"&A4","v":"x = Test Score"},{"$f":"B15&\" = \"&ROUND(C15,4)","v":"P(X>=10) = 0.1587"},{"$f":"\"P(x<=\"&C4&\") = \"&ROUND(C10,4)","v":"P(x<=14) = 0.8413"}]
[null,null,null,null,{"$f":"(F20-$C$7)/$C$8","v":-6},0,{"$f":"_xlfn.NORM.DIST(F20,$C$7,$C$8,0)","v":3.037941424911643E-9},{"$f":"IF(F20<=$C$4,G20,\"\")","v":3.037941424911643E-9},null,"F17 has the formula:\n=NORM.DIST(E20,$C$7,$C$8,0)\nG17 has the formula:\n=IF(E20<=$C$4,F20,\"\")"]
[null,null,null,null,{"$f":"(F21-$C$7)/$C$8","v":-5.95},0.1,{"$f":"_xlfn.NORM.DIST(F21,$C$7,$C$8,0)","v":4.0956692017395868E-9},{"$f":"IF(F21<=$C$4,G21,\"\")","v":4.0956692017395868E-9}]
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[null,null,null,null,-5.85,0.30000000000000004,7.3885397932400267E-9,7.3885397932400267E-9]
[null,{"$f":"\"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(\"&C5&C4&\") = P(\"&LEFT(C5,1)&C4&\")\"","v":"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(<=14) = P(<14)"},null,null,-5.8,0.4,9.8865982031223359E-9,9.8865982031223359E-9]
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[null,null,null,null,-5.7,0.60000000000000009,1.756977547410217E-8,1.756977547410217E-8]
[null,null,null,null,-5.65,0.70000000000000007,2.333443398797128E-8,2.333443398797128E-8,null,"Chart Steps:"]
[null,null,null,null,-5.6,0.8,3.0913102500829286E-8,3.0913102500829286E-8,null,"Create Chart Label in cell F17: =\"Bell Curve For Test Scores, mew = \"&C7&\", sigma = \"&C8"]
[null,null,null,null,-5.55,0.9,4.0850951892716102E-8,4.0850951892716102E-8,null,"Create series label in cell G19: =\"Remaining Area = \"&ROUND(1-C10,4)"]
[null,null,null,null,-5.5,1,5.384880021271638E-8,5.384880021271638E-8,null,"Create series label in cell H19: =\"P(x<=\"&C4&\") = \"&ROUND(C10,4)"]
[null,null,null,null,-5.45,1.1000000000000001,7.0805035650805879E-8,7.0805035650805879E-8,null,"Create x values (type 0, right-click fill handle, Series, Columns, Step .01, End = 24, Ok)"]
[null,null,null,null,-5.4,1.2000000000000002,9.2868092227764484E-8,9.2868092227764484E-8,null,"Create z values"]
[null,null,null,null,-5.35,1.3,1.2150192705402675E-7,1.2150192705402675E-7,null,"Plot Height Values with Area Chart"]
[null,null,null,null,-5.3,1.4000000000000001,1.585674608357988E-7,1.585674608357988E-7,null,"Edit horizontal Axis (ChartTools Design tab Ribbon, Select Data button)"]
[null,null,null,null,-5.25,1.5,2.0642354943149992E-7,2.0642354943149992E-7,null,"Plot Secondary Heights"]
[null,null,null,null,-5.2,1.6,2.6805176723488073E-7,2.6805176723488073E-7,null,"Right-click secondary Heights on chart and Ctrl + 1 to open Format Chart Element dialog box, change series to secondary axis."]
[null,null,null,null,-5.15,1.7000000000000002,3.4721011769276696E-7,3.4721011769276696E-7,null,"Delete Vertical Axis on right"]
[null,null,null,null,-5.0999999999999996,1.8,4.4862175811916687E-7,4.4862175811916687E-7,null,"ChartTools Layout tab Ribbon, \"Axes\" button in Axes group, Secondary Horizontal Axis, Show Left to Right Axis"]
[null,null,null,null,-5.05,1.9000000000000001,5.782059517898917E-7,5.782059517898917E-7,null,"Click on Axis, Ctrl + 1, Axis Options, Axis Labels = Low"]
[null,null,null,null,-5,2,7.4335975736714884E-7,7.4335975736714884E-7,null,"Move Legend"]
[null,null,null,null,-4.95,2.1,9.5330045156140538E-7,9.5330045156140538E-7,null,"Add Chart Title linked to cell"]
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[null,null,null,null,-2.8,6.4,3.9577257914899843E-3,3.9577257914899843E-3]
[null,null,null,null,{"$f":"(F85-$C$7)/$C$8","v":-2.75},6.5,{"$f":"_xlfn.NORM.DIST(F85,$C$7,$C$8,0)","v":4.5467812507955264E-3},{"$f":"IF(F85<=$C$4,G85,\"\")","v":4.5467812507955264E-3}]
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[null,null,null,null,-2.5999999999999996,6.8000000000000007,6.7914846168428168E-3,6.7914846168428168E-3]
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[null,null,null,null,-2.5,7,8.7641502467842702E-3,8.7641502467842702E-3]
[null,null,null,null,-2.4499999999999997,7.1000000000000005,9.9186771958976686E-3,9.9186771958976686E-3]
[null,null,null,null,-2.4,7.2,1.119726514742145E-2,1.119726514742145E-2]
[null,null,null,null,-2.3499999999999996,7.3000000000000007,1.2609109957597208E-2,1.2609109957597208E-2]
[null,null,null,null,-2.2999999999999998,7.4,1.4163518870800593E-2,1.4163518870800593E-2]
[null,null,null,null,-2.25,7.5,1.5869825917833709E-2,1.5869825917833709E-2]
[null,null,null,null,-2.1999999999999997,7.6000000000000005,1.773729642311573E-2,1.773729642311573E-2]
[null,null,null,null,-2.15,7.7,1.977502079468511E-2,1.977502079468511E-2]
[null,null,null,null,-2.0999999999999996,7.8000000000000007,2.1991797990213616E-2,2.1991797990213616E-2]
[null,null,null,null,-2.0499999999999998,7.9,2.4396009289591382E-2,2.4396009289591382E-2]
[null,null,null,null,-2,8,2.6995483256594031E-2,2.6995483256594031E-2]
[null,null,null,null,-1.9500000000000002,8.1,2.9797353034408027E-2,2.9797353034408027E-2]
[null,null,null,null,-1.8999999999999995,8.2000000000000011,3.2807907387338332E-2,3.2807907387338332E-2]
[null,null,null,null,-1.8499999999999996,8.3000000000000007,3.603243716810902E-2,3.603243716810902E-2]
[null,null,null,null,-1.7999999999999998,8.4,3.9475079150447089E-2,3.9475079150447089E-2]
[null,null,null,null,-1.75,8.5,4.3138659413255766E-2,4.3138659413255766E-2]
[null,null,null,null,-1.7000000000000002,8.6,4.7024538688443453E-2,4.7024538688443453E-2]
[null,null,null,null,-1.6499999999999995,8.7000000000000011,5.1132462281989047E-2,5.1132462281989047E-2]
[null,null,null,null,-1.5999999999999996,8.8000000000000007,5.5460417339727813E-2,5.5460417339727813E-2]
[null,null,null,null,-1.5499999999999998,8.9,6.0004500348492827E-2,6.0004500348492827E-2]
[null,null,null,null,-1.5,9,6.4758797832945872E-2,6.4758797832945872E-2]
[null,null,null,null,-1.4500000000000002,9.1,6.9715283222680113E-2,6.9715283222680113E-2]
[null,null,null,null,-1.3999999999999995,9.2000000000000011,7.4863732817872494E-2,7.4863732817872494E-2]
[null,null,null,null,-1.3499999999999996,9.3000000000000007,8.019166367095984E-2,8.019166367095984E-2]
[null,null,null,null,-1.2999999999999998,9.4,8.5684296023903705E-2,8.5684296023903705E-2]
[null,null,null,null,-1.25,9.5,9.1324542694510957E-2,9.1324542694510957E-2]
[null,null,null,null,-1.1999999999999993,9.6000000000000014,9.7093027491606559E-2,9.7093027491606559E-2]
[null,null,null,null,-1.1499999999999995,9.7000000000000011,0.10296813435998746,0.10296813435998746]
[null,null,null,null,-1.0999999999999996,9.8000000000000007,0.10892608851627532,0.10892608851627532]
[null,null,null,null,-1.0499999999999998,9.9,0.11494107034211655,0.11494107034211655]
[null,null,null,null,-1,10,0.12098536225957168,0.12098536225957168]
[null,null,null,null,-0.94999999999999929,10.100000000000001,0.12702952823459457,0.12702952823459457]
[null,null,null,null,-0.89999999999999947,10.200000000000001,0.13304262494937749,0.13304262494937749]
[null,null,null,null,-0.84999999999999964,10.3,0.13899244306549829,0.13899244306549829]
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[null,null,null,null,-0.75,10.5,0.15056871607740221,0.15056871607740221]
[null,null,null,null,-0.69999999999999929,10.600000000000001,0.15612696668338072,0.15612696668338072]
[null,null,null,null,-0.64999999999999947,10.700000000000001,0.16148617983395722,0.16148617983395722]
[null,null,null,null,-0.59999999999999964,10.8,0.16661230144589986,0.16661230144589986]
[null,null,null,null,-0.54999999999999982,10.9,0.17147192750969195,0.17147192750969195]
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[null,null,null,null,-0.34999999999999964,11.3,0.18762017345846899,0.18762017345846899]
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[null,null,null,null,{"$f":"(F149-$C$7)/$C$8","v":0.45000000000000018},12.9,{"$f":"_xlfn.NORM.DIST(F149,$C$7,$C$8,0)","v":0.18026348123082397},{"$f":"IF(F149<=$C$4,G149,\"\")","v":0.18026348123082397}]
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[null,"Total is not 1 because not Probability",null,null,4.1000000000000014,20.200000000000003,4.4630828588566152E-5,""]
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{"sheet":">=","index":15,"n_rows":259,"n_cols":9,"rows_kept":259,"cut":false,"hidden":false,"merged":[[12,1,19,1],[20,1,25,1],[16,8,21,11]]}
["Based on past data, estimate the percentage of scores on the next statistics test that will be 15 or more. What should we do if 37% get a score of 15 or more?"]
["Test Score","x",15]
[null,"Operator 1",">=",null,{"$f":"B5&\" \"&C5&\", \"&B6&\" \"&C6","v":"Test Score = mean = mew = μ = 12, standard deviation = sigma = σ = 2"}]
[null,"Operator 2"]
[null,"Test Score = mean = mew = μ =",12]
[null,"standard deviation = sigma = σ =",2]
[null,"Z"]
[null,{"$f":"\"p(X \"&$C$3&\" \"&C2&\")\"","v":"p(X >= 15)"}]
[null,{"$f":"\"p(Z \"&C3&\" \"&C7&\")\"","v":"p(Z >= )"}]
[null,"What is x given cumulative Probability?"]
[null,"What is z given cumulative Probability?"]
[null,"X from Z"]
[null,{"$f":"IF(C8<>\"\",\"Based on past data it would be reasonable to assume that \"&TEXT(C8,\"0.00%\")&\" of all the scores on the next text will be \"&C2&\" or more. If we then run the test and \"&TEXT(C8+0.3,\"0%\")&\" of the tests are above \"&C2&\", we would need to investigate why.\",\"\")","v":""},null,"upper",0.05]
[null,null,null,"Lower",0.05]
[null,null,null,null,null,"Height of curve"]
[null,null,null,null,{"$f":"B2&\" = \"&A2","v":"x = Test Score"},"Remaining Area",{"$f":"\"Area for\"&C3&C2","v":"Area for>=15"}]
[null,null,null,null,0,null,null,null,"F17 has the formula:\n=NORM.DIST(E17,$C$5,$C$6,0)\nG17 has the formula:\n=IF(E17>=$C$2,F17,\"\")"]
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[null,{"$f":"\"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(\"&C3&C2&\") = P(\"&LEFT(C3,1)&C2&\")\"","v":"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(>=15) = P(>15)"},null,null,0.4]
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[]
[null,"Total is not 1 because not Probability",null,null,null,{"$f":"SUM(F17:F258)","v":0}]

{"sheet":">= (an)","index":16,"n_rows":259,"n_cols":9,"rows_kept":259,"cut":false,"hidden":false,"merged":[[12,1,19,1],[16,8,21,11],[20,1,25,1]]}
["Based on past data, estimate the percentage of scores on the next statistics test that will be 15 or more. What should we do if 37% get a score of 15 or more?"]
["Test Score","x",15]
[null,"Operator 1",">=",null,{"$f":"B5&\" \"&C5&\", \"&B6&\" \"&C6","v":"Test Score = mean = mew = μ = 12, standard deviation = sigma = σ = 2"}]
[null,"Operator 2"]
[null,"Test Score = mean = mew = μ =",12]
[null,"standard deviation = sigma = σ =",2]
[null,"Z",{"$f":"(C2-C5)/C6","v":1.5}]
[null,{"$f":"\"p(X \"&$C$3&\" \"&C2&\")\"","v":"p(X >= 15)"},{"$f":"1-_xlfn.NORM.DIST(C2,C5,C6,1)","v":6.6807201268858085E-2}]
[null,{"$f":"\"p(Z \"&C3&\" \"&C7&\")\"","v":"p(Z >= 1.5)"},{"$f":"1-_xlfn.NORM.S.DIST(C7,1)","v":6.6807201268858085E-2}]
[null,"What is x given cumulative Probability?",{"$f":"_xlfn.NORM.INV(1-C8,C5,C6)","v":15}]
[null,"What is z given cumulative Probability?",{"$f":"_xlfn.NORM.S.INV(1-C9)","v":1.5}]
[null,"X from Z",{"$f":"C5+C6*C11","v":15}]
[null,{"$f":"IF(C8<>\"\",\"Based on past data it would be reasonable to assume that \"&TEXT(C8,\"0.00%\")&\" of all the scores on the next text will be \"&C2&\" or more. If we then run the test and \"&TEXT(C8+0.3,\"0%\")&\" of the tests are above \"&C2&\", we would need to investigate why.\",\"\")","v":"Based on past data it would be reasonable to assume that 6.68% of all the scores on the next text will be 15 or more. If we then run the test and 37% of the tests are above 15, we would need to investigate why."},null,"upper",0.05,{"$f":"_xlfn.NORM.INV(1-E13,C5,C6)","v":15.289707253902943}]
[null,null,null,"Lower",0.05,{"$f":"_xlfn.NORM.INV(E14,C5,C6)","v":8.7102927460970552}]
[null,null,null,null,null,"Height of curve"]
[null,null,null,null,{"$f":"B2&\" = \"&A2","v":"x = Test Score"},"Remaining Area",{"$f":"\"Area for\"&C3&C2","v":"Area for>=15"}]
[null,null,null,null,0,{"$f":"_xlfn.NORM.DIST(E17,$C$5,$C$6,0)","v":3.037941424911643E-9},{"$f":"IF(E17>=$C$2,F17,\"\")","v":""},null,"F17 has the formula:\n=NORM.DIST(E17,$C$5,$C$6,0)\nG17 has the formula:\n=IF(E17>=$C$2,F17,\"\")"]
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[null,null,null,null,15.1,6.0004500348492827E-2,6.0004500348492827E-2]
[null,null,null,null,15.2,5.5460417339727813E-2,5.5460417339727813E-2]
[null,null,null,null,15.3,5.1132462281988984E-2,5.1132462281988984E-2]
[null,null,null,null,15.4,4.7024538688443453E-2,4.7024538688443453E-2]
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[null,null,null,null,17.3,5.9561218038025844E-3,5.9561218038025844E-3]
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[null,null,null,null,23.4,1.7569775474102233E-8,1.7569775474102233E-8]
[null,null,null,null,23.5,1.3196216017852868E-8,1.3196216017852868E-8]
[null,null,null,null,23.6,9.8865982031223012E-9,9.8865982031223012E-9]
[null,null,null,null,23.7,7.3885397932400267E-9,7.3885397932400267E-9]
[null,null,null,null,23.8,5.5078818123411542E-9,5.5078818123411542E-9]
[null,null,null,null,23.9,4.0956692017396158E-9,4.0956692017396158E-9]
[null,null,null,null,24,3.037941424911643E-9,3.037941424911643E-9]
[]
[null,"Total is not 1 because not Probability",null,null,null,{"$f":"SUM(F17:F258)","v":9.9999999831545026}]

{"sheet":"<=x<=","index":17,"n_rows":257,"n_cols":9,"rows_kept":257,"cut":false,"hidden":false,"merged":[[12,1,16,1],[17,1,22,1],[16,8,21,11]]}
[{"$f":"\"Based on past data, estimate the percentage of scores on the next statistics test that will be between \"&C2&\" and \"&C3&\" if mew is \"&C6&\" and sigma is \"&C7&\"?\"","v":"Based on past data, estimate the percentage of scores on the next statistics test that will be between 12 and 13.75 if mew is 12 and sigma is 2?"}]
["Test Score","x1",12]
[null,"x2",13.75]
[null,"Operator 1",">="]
[null,"Operator 2","<="]
[null,"mean = mew = μ =",12]
[null,"standard deviation = sigma = σ =",2]
[null,"z1"]
[null,"z2"]
["AND",{"$f":"\"P(\"&$C$2&$C$5&\" x \"&$C$5&$C$3&\")\"","v":"P(12<= x <=13.75)"}]
["AND",{"$f":"\"P(\"&($C$2-C6)/C7&$C$5&\" z \"&$C$5&($C$3-C6)/C7&\")\"","v":"P(0<= z <=0.875)"}]
["OR",{"$f":"\"P(x < \"&C2&\" OR x > \"&C3&\") = \"","v":"P(x < 12 OR x > 13.75) = "}]
[null,{"$f":"IF(C10<>\"\",\"Based on past data it would be reasonable to assume that \"&TEXT(C10,\"0.00%\")&\" of all the scores on the next text will be between \"&C2&\" and \"&C3&\".\",\"\")","v":""}]
[null,null,null,null,null,null,null,"To see how to create charts with labels like seen in this video see video title \"Excel 2010 Statistics 58: Normal Distribution Bell Curve Area Chart With X and Z Values – Many Tricks\""]
[null,null,null,null,null,"Height of curve"]
[null,null,null,null,"x = Test Score",{"$f":"B12&ROUND(C12,4)","v":"P(x < 12 OR x > 13.75) = 0"},{"$f":"B10&\" = \"&ROUND(C10,4)","v":"P(12<= x <=13.75) = 0"}]
[null,null,null,null,0,null,null,null,"F17 has the formula:\n=NORM.DIST(E17,$C$6,$C$7,0)\nG17 has the formula:\n=IF(AND(E17>=$C$2,E17<=$C$3),F17,\"\")"]
[null,{"$f":"\"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(\"&C4&C2&\") = P(\"&LEFT(C4,1)&C2&\")\"","v":"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(>=12) = P(>12)"},null,null,0.1]
[null,null,null,null,0.2]
[null,null,null,null,0.3]
[null,null,null,null,0.4]
[null,null,null,null,0.5]
[null,null,null,null,0.6]
[null,null,null,null,0.7]
[null,null,null,null,0.8]
[null,null,null,null,0.9]
[null,null,null,null,1]
[null,null,null,null,1.1000000000000001]
[null,null,null,null,1.2]
[null,null,null,null,1.3]
[null,null,null,null,1.4]
[null,null,null,null,1.5]
[null,null,null,null,1.6]
[null,null,null,null,1.7]
[null,null,null,null,1.8]
[null,null,null,null,1.9]
[null,null,null,null,2]
[null,null,null,null,2.1]
[null,null,null,null,2.2000000000000002]
[null,null,null,null,2.2999999999999998]
[null,null,null,null,2.4]
[null,null,null,null,2.5]
[null,null,null,null,2.6]
[null,null,null,null,2.7]
[null,null,null,null,2.8]
[null,null,null,null,2.9]
[null,null,null,null,3]
[null,null,null,null,3.1]
[null,null,null,null,3.2]
[null,null,null,null,3.3]
[null,null,null,null,3.4]
[null,null,null,null,3.5]
[null,null,null,null,3.6]
[null,null,null,null,3.7]
[null,null,null,null,3.8]
[null,null,null,null,3.9]
[null,null,null,null,4]
[null,null,null,null,4.0999999999999996]
[null,null,null,null,4.2]
[null,null,null,null,4.3]
[null,null,null,null,4.4000000000000004]
[null,null,null,null,4.5]
[null,null,null,null,4.5999999999999996]
[null,null,null,null,4.7]
[null,null,null,null,4.8]
[null,null,null,null,4.9000000000000004]
[null,null,null,null,5]
[null,null,null,null,5.0999999999999996]
[null,null,null,null,5.2]
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[null,null,null,null,5.4]
[null,null,null,null,5.5]
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[null,null,null,null,5.7]
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[null,null,null,null,5.9]
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[null,null,null,null,6.5]
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[null,null,null,null,6.8]
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[null,null,null,null,7.6]
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[null,null,null,null,7.9]
[null,null,null,null,8]
[null,null,null,null,8.1]
[null,null,null,null,8.1999999999999993]
[null,null,null,null,8.3000000000000007]
[null,null,null,null,8.4]
[null,null,null,null,8.5]
[null,null,null,null,8.6]
[null,null,null,null,8.6999999999999993]
[null,null,null,null,8.8000000000000007]
[null,null,null,null,8.9]
[null,null,null,null,9]
[null,null,null,null,9.1]
[null,null,null,null,9.1999999999999993]
[null,null,null,null,9.3000000000000007]
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[null,null,null,null,9.6999999999999993]
[null,null,null,null,9.8000000000000007]
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[null,null,null,null,10.199999999999999]
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[null,null,null,null,12.4]
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[null,null,null,null,12.6]
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[null,null,null,null,15.7]
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[null,null,null,null,16]
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[null,null,null,null,21.5]
[null,null,null,null,21.6]
[null,null,null,null,21.7]
[null,null,null,null,21.8]
[null,null,null,null,21.9]
[null,null,null,null,22]
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[null,null,null,null,22.2]
[null,null,null,null,22.3]
[null,null,null,null,22.4]
[null,null,null,null,22.5]
[null,null,null,null,22.6]
[null,null,null,null,22.7]
[null,null,null,null,22.8]
[null,null,null,null,22.9]
[null,null,null,null,23]
[null,null,null,null,23.1]
[null,null,null,null,23.2]
[null,null,null,null,23.3]
[null,null,null,null,23.4]
[null,null,null,null,23.5]
[null,null,null,null,23.6]
[null,null,null,null,23.7]
[null,null,null,null,23.8]
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[null,null,null,null,24]

{"sheet":"<=x<= (an)","index":18,"n_rows":257,"n_cols":9,"rows_kept":257,"cut":false,"hidden":false,"merged":[[12,1,16,1],[16,8,21,11],[17,1,22,1]]}
[{"$f":"\"Based on past data, estimate the percentage of scores on the next statistics test that will be between \"&C2&\" and \"&C3&\" if mew is \"&C6&\" and sigma is \"&C7&\"?\"","v":"Based on past data, estimate the percentage of scores on the next statistics test that will be between 8 and 16 if mew is 12 and sigma is 2?"}]
["Test Score","x1",8]
[null,"x2",16]
[null,"Operator 1",">="]
[null,"Operator 2","<="]
[null,"mean = mew = μ =",12]
[null,"standard deviation = sigma = σ =",2]
[null,"z1",{"$f":"(C2-$C$6)/$C$7","v":-2}]
[null,"z2",{"$f":"(C3-$C$6)/$C$7","v":2}]
["AND",{"$f":"\"P(\"&$C$2&$C$5&\" x \"&$C$5&$C$3&\")\"","v":"P(8<= x <=16)"},{"$f":"_xlfn.NORM.DIST(C3,C6,C7,1)-_xlfn.NORM.DIST(C2,C6,C7,1)","v":0.95449973610364158}]
["AND",{"$f":"\"P(\"&($C$2-C6)/C7&$C$5&\" z \"&$C$5&($C$3-C6)/C7&\")\"","v":"P(-2<= z <=2)"},{"$f":"_xlfn.NORM.S.DIST(C9,1)-_xlfn.NORM.S.DIST(C8,1)","v":0.95449973610364158}]
["OR",{"$f":"\"P(x < \"&C2&\" OR x > \"&C3&\") = \"","v":"P(x < 8 OR x > 16) = "},{"$f":"1-C10","v":4.5500263896358417E-2}]
[null,{"$f":"IF(C10<>\"\",\"Based on past data it would be reasonable to assume that \"&TEXT(C10,\"0.00%\")&\" of all the scores on the next text will be between \"&C2&\" and \"&C3&\".\",\"\")","v":"Based on past data it would be reasonable to assume that 95.45% of all the scores on the next text will be between 8 and 16."}]
[null,null,null,null,null,null,null,"To see how to create charts with labels like seen in this video see video title \"Excel 2010 Statistics 58: Normal Distribution Bell Curve Area Chart With X and Z Values – Many Tricks\""]
[null,null,null,null,null,"Height of curve"]
[null,null,null,null,"x = Test Score",{"$f":"B12&ROUND(C12,4)","v":"P(x < 8 OR x > 16) = 0.0455"},{"$f":"B10&\" = \"&ROUND(C10,4)","v":"P(8<= x <=16) = 0.9545"}]
[null,null,null,null,0,{"$f":"_xlfn.NORM.DIST(E17,$C$6,$C$7,0)","v":3.037941424911643E-9},{"$f":"IF(AND(E17>=$C$2,E17<=$C$3),F17,\"\")","v":""},null,"F17 has the formula:\n=NORM.DIST(E17,$C$6,$C$7,0)\nG17 has the formula:\n=IF(AND(E17>=$C$2,E17<=$C$3),F17,\"\")"]
[null,{"$f":"\"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(\"&C4&C2&\") = P(\"&LEFT(C4,1)&C2&\")\"","v":"Note: Because we are dealing with continuous random variables and we are calculating probability from area and because the area of a  line is zero, P(>=8) = P(>8)"},null,null,0.1,{"$f":"_xlfn.NORM.DIST(E18,$C$6,$C$7,0)","v":4.0956692017395868E-9},{"$f":"IF(AND(E18>=$C$2,E18<=$C$3),F18,\"\")","v":""}]
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[null,null,null,null,2.9,6.3736661909167328E-6,""]
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[null,null,null,null,3.5,2.3859318270602476E-5,""]
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[null,null,null,null,5.0999999999999996,5.1914064783070517E-4,""]
[null,null,null,null,5.2,6.1610958423650997E-4,""]
[null,null,null,null,5.3,7.2936540233337294E-4,""]
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[null,null,null,null,6.6,5.2104674072112958E-3,""]
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[null,null,null,null,6.8,6.7914846168428064E-3,""]
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[{"$f":"\"If the professor grades with a bell curve and assigns a grade of A for the top \"&TEXT(Y6,\"0.00%\")&\" of the scores, what score would you need to get to earn an A if the mean (from past data) was \"&Y4&\" and the standard deviation (from past data) was \"&Y5&\"?\"","v":"If the professor grades with a bell curve and assigns a grade of A for the top 5.00% of the scores, what score would you need to get to earn an A if the mean (from past data) was 79 and the standard deviation (from past data) was 6?"}]
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[]
[{"$f":"\"From past population data that has a normal shaped distribution, if the employees on average produced \"&Y14&\" boomerangs per day with a standard deviation of \"&Y15&\" how many boomerangs would have to be produced for the day's production level to be among the slowest \"&TEXT(Y16,\"0.00%\")&\" of days?\"","v":"From past population data that has a normal shaped distribution, if the employees on average produced 1000 boomerangs per day with a standard deviation of 50 how many boomerangs would have to be produced for the day's production level to be among the slowest 10.00% of days?"}]
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{"sheet":"Find X (an)","index":20,"n_rows":6024,"n_cols":25,"rows_kept":6024,"cut":false,"hidden":false,"merged":[]}
[{"$f":"\"If the professor grades with a bell curve and assigns a grade of A for the top \"&TEXT(Y6,\"0.00%\")&\" of the scores, what score would you need to get to earn an A if the mean (from past data) was \"&Y4&\" and the standard deviation (from past data) was \"&Y5&\"?\"","v":"If the professor grades with a bell curve and assigns a grade of A for the top 5.00% of the scores, what score would you need to get to earn an A if the mean (from past data) was 79 and the standard deviation (from past data) was 6?"}]
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[]
[{"$f":"\"From past population data that has a normal shaped distribution, if the employees on average produced \"&Y14&\" boomerangs per day with a standard deviation of \"&Y15&\" how many boomerangs would have to be produced for the day's production level to be among the slowest \"&TEXT(Y16,\"0.00%\")&\" of days?\"","v":"From past population data that has a normal shaped distribution, if the employees on average produced 1000 boomerangs per day with a standard deviation of 50 how many boomerangs would have to be produced for the day's production level to be among the slowest 10.00% of days?"}]
[]
["What is x?","# units produced",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Data For Questions"]
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["z",{"$f":"_xlfn.NORM.S.INV(B16)","v":-1.2815515655446006},null,null,"x = z*sigma+mu"]
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[]
[]
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["x",75000,null,null,null,null,null,null,23500,8.1913384034791727E-13,"",null,23500,3.3560855964953859E-14,3.3560855964953859E-14,null,23500,3.3560855964953859E-14,""]
["Comparative Operator","x<=",null,null,null,null,null,null,23550,8.438586377327511E-13,"",null,23550,3.460843187680675E-14,3.460843187680675E-14,null,23550,3.460843187680675E-14,""]
[{"$f":"\"P(\"&B13&DOLLAR(B12,0)&\") = \"","v":"P(x<=$75,000) = "},null,null,null,null,null,null,null,23600,8.6930799728801739E-13,"",null,23600,3.5687897794155882E-14,3.5687897794155882E-14,null,23600,3.5687897794155882E-14,""]
[null,null,null,null,null,null,null,null,23650,8.9550247895255875E-13,"",null,23650,3.6800198674641445E-14,3.6800198674641445E-14,null,23650,3.6800198674641445E-14,""]
["Oakland, CA","Pop Data approximately Bell Shaped",null,null,null,null,null,null,23700,9.2246320572827211E-13,"",null,23700,3.7946306670420244E-14,3.7946306670420244E-14,null,23700,3.7946306670420244E-14,""]
[{"$f":"A16&\" Accounting Manager Average Annual Salary\"","v":"Oakland, CA Accounting Manager Average Annual Salary"},94500,null,null,null,null,null,null,23750,9.5021187850260191E-13,"",null,23750,3.9127221886200303E-14,3.9127221886200303E-14,null,23750,3.9127221886200303E-14,""]
["Sigma",11000,null,null,null,null,null,null,23800,9.7877079124411786E-13,"",null,23800,4.0343973157674084E-14,4.0343973157674084E-14,null,23800,4.0343973157674084E-14,""]
["Upper x",80000,null,null,null,null,null,null,23850,1.0081628465801567E-12,"",null,23850,4.159761885087867E-14,4.159761885087867E-14,null,23850,4.159761885087867E-14,""]
["Lower x",100000,null,null,null,null,null,null,23900,1.0384115717656326E-12,"",null,23900,4.2889247683022344E-14,4.2889247683022344E-14,null,23900,4.2889247683022344E-14,""]
["Comparative Operator"," <= x <= ",null,null,null,null,null,null,23950,1.0695411350523283E-12,"",null,23950,4.4219979565332407E-14,4.4219979565332407E-14,null,23950,4.4219979565332407E-14,""]
[{"$f":"\"P(\"&DOLLAR(B19,0)&B21&DOLLAR(B20,0)&\") = \"","v":"P($80,000 <= x <= $100,000) = "},null,null,null,null,null,null,null,24000,1.1015763624682309E-12,"",null,24000,4.5590966468493575E-14,4.5590966468493575E-14,null,24000,4.5590966468493575E-14,""]
[null,null,null,null,null,null,null,null,24050,1.1345427550166375E-12,"",null,24050,4.7003393311255776E-14,4.7003393311255776E-14,null,24050,4.7003393311255776E-14,""]
["Frozen Corn Bag Filling Machine weight follows a normal distribution",null,null,null,null,null,null,null,24100,1.1684665063049869E-12,"",null,24100,4.8458478872809898E-14,4.8458478872809898E-14,null,24100,4.8458478872809898E-14,""]
["Mean weight of package",16,"oz.",null,null,null,null,null,24150,1.2033745206136439E-12,"",null,24150,4.9957476729542026E-14,4.9957476729542026E-14,null,24150,4.9957476729542026E-14,""]
["Sigma",0.3,"oz.",null,null,null,null,null,24200,1.239294431415013E-12,"",null,24200,5.150167621679003E-14,5.150167621679003E-14,null,24200,5.150167621679003E-14,""]
["What is probability of getting between +/- 1.96 Standard Deviations?",1.96,null,null,null,null,null,null,24250,1.2762546203536441E-12,"",null,24250,5.3092403416246521E-14,5.3092403416246521E-14,null,24250,5.3092403416246521E-14,""]
["What are the two x values of weight that bookend the +/- 1.96 Standard Deviations?",null,null,null,null,null,null,null,24300,1.3142842366982141E-12,"",null,24300,5.4731022169663593E-14,5.4731022169663593E-14,null,24300,5.4731022169663593E-14,""]
["Lower",null,null,null,null,null,null,null,24350,1.353413217276506E-12,"",null,24350,5.6418935119531527E-14,5.6418935119531527E-14,null,24350,5.6418935119531527E-14,""]
["Upper",null,null,null,null,null,null,null,24400,1.3936723069047391E-12,"",null,24400,5.8157584777422871E-14,5.8157584777422871E-14,null,24400,5.8157584777422871E-14,""]
[{"$f":"A27","v":"What is probability of getting between +/- 1.96 Standard Deviations?"},null,null,null,null,null,null,null,24450,1.435093079322912E-12,"",null,24450,5.9948454620704652E-14,5.9948454620704652E-14,null,24450,5.9948454620704652E-14,""]
["What is probability of NOT getting between +/- 1.96 Standard Deviations?",null,null,{"$f":"1-(_xlfn.NORM.DIST(B30,B25,B26,1)-_xlfn.NORM.DIST(B29,B25,B26,1))","v":1},null,null,null,null,24500,1.4777079586480055E-12,"",null,24500,6.1793070218348656E-14,6.1793070218348656E-14,null,24500,6.1793070218348656E-14,""]
[null,null,null,null,null,null,null,null,24550,1.5215502413571453E-12,"",null,24550,6.3693000386572383E-14,6.3693000386572383E-14,null,24550,6.3693000386572383E-14,""]
["Nielsen Reports",null,null,null,null,null,null,null,24600,1.5666541188132573E-12,"",null,24600,6.564985837507706E-14,6.564985837507706E-14,null,24600,6.564985837507706E-14,""]
["Mean daily TV watched per household",8.4,"hours",null,null,null,null,null,24650,1.6130547003457386E-12,"",null,24650,6.7665303084654466E-14,6.7665303084654466E-14,null,24650,6.7665303084654466E-14,""]
[{"$f":"\"If distribution normal with SD of \"&B36&\" hours\"","v":"If distribution normal with SD of 2.5 hours"},2.5,"hours",null,null,null,null,null,24700,1.6607880368992045E-12,"",null,24700,6.9741040316965009E-14,6.9741040316965009E-14,null,24700,6.9741040316965009E-14,""]
[{"$f":"\"P(Hours Watched Per Day \"&D37&C37&\" hours) = \"","v":"P(Hours Watched Per Day >=10 hours) = "},null,10,">=",null,null,null,null,24750,1.7098911452635135E-12,"",null,24750,7.1878824057295551E-14,7.1878824057295551E-14,null,24750,7.1878824057295551E-14,""]
[{"$f":"\"# Hours Watched per Day to be in lowest \"&TEXT(C38,\"0%\")","v":"# Hours Watched per Day to be in lowest 1%"},null,0.01,null,null,null,null,null,24800,1.7604020328985782E-12,"",null,24800,7.4080457791139954E-14,7.4080457791139954E-14,null,24800,7.4080457791139954E-14,""]
[{"$f":"\"P(x\"&D39&C39&\") = \"","v":"P(x<=1) = "},null,1,"<=",null,null,null,null,24850,1.8123597233678709E-12,"",null,24850,7.6347795855451327E-14,7.6347795855451327E-14,null,24850,7.6347795855451327E-14,""]
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[null,null,null,null,null,null,null,null,25800,3.1347273817919788E-12,"",null,25800,1.3479986888131017E-13,1.3479986888131017E-13,null,25800,1.3479986888131017E-13,""]
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["Seattle, WA","Pop Data approximately Bell Shaped",null,null,null,null,null,null,23350,7.4910936663715652E-13,"",null,23350,3.0600411237725157E-14,3.0600411237725157E-14,null,23350,3.0600411237725157E-14,""]
[{"$f":"A9&\" Accounting Manager Average Annual Salary\"","v":"Seattle, WA Accounting Manager Average Annual Salary"},91300,null,null,null,null,null,null,23400,7.7177842125705293E-13,"",null,23400,3.1557725890233816E-14,3.1557725890233816E-14,null,23400,3.1557725890233816E-14,""]
["Sigma",10500,null,null,null,null,null,null,23450,7.9511359379968727E-13,"",null,23450,3.2544251557322553E-14,3.2544251557322553E-14,null,23450,3.2544251557322553E-14,""]
["x",75000,null,null,null,null,null,null,23500,8.1913384034791727E-13,"",null,23500,3.3560855964953859E-14,3.3560855964953859E-14,null,23500,3.3560855964953859E-14,""]
["Comparative Operator","x<=",null,null,null,null,null,null,23550,8.438586377327511E-13,"",null,23550,3.460843187680675E-14,3.460843187680675E-14,null,23550,3.460843187680675E-14,""]
[{"$f":"\"P(\"&B13&DOLLAR(B12,0)&\") = \"","v":"P(x<=$75,000) = "},{"$f":"_xlfn.NORM.DIST(B12,B10,B11,1)","v":6.0285549157761395E-2},null,null,null,null,null,null,23600,8.6930799728801739E-13,"",null,23600,3.5687897794155882E-14,3.5687897794155882E-14,null,23600,3.5687897794155882E-14,""]
[null,null,null,null,null,null,null,null,23650,8.9550247895255875E-13,"",null,23650,3.6800198674641445E-14,3.6800198674641445E-14,null,23650,3.6800198674641445E-14,""]
["Oakland, CA","Pop Data approximately Bell Shaped",null,null,null,null,null,null,23700,9.2246320572827211E-13,"",null,23700,3.7946306670420244E-14,3.7946306670420244E-14,null,23700,3.7946306670420244E-14,""]
[{"$f":"A16&\" Accounting Manager Average Annual Salary\"","v":"Oakland, CA Accounting Manager Average Annual Salary"},94500,null,null,null,null,null,null,23750,9.5021187850260191E-13,"",null,23750,3.9127221886200303E-14,3.9127221886200303E-14,null,23750,3.9127221886200303E-14,""]
["Sigma",11000,null,null,null,null,null,null,23800,9.7877079124411786E-13,"",null,23800,4.0343973157674084E-14,4.0343973157674084E-14,null,23800,4.0343973157674084E-14,""]
["Upper x",80000,null,null,null,null,null,null,23850,1.0081628465801567E-12,"",null,23850,4.159761885087867E-14,4.159761885087867E-14,null,23850,4.159761885087867E-14,""]
["Lower x",100000,null,null,null,null,null,null,23900,1.0384115717656326E-12,"",null,23900,4.2889247683022344E-14,4.2889247683022344E-14,null,23900,4.2889247683022344E-14,""]
["Comparative Operator"," <= x <= ",null,null,null,null,null,null,23950,1.0695411350523283E-12,"",null,23950,4.4219979565332407E-14,4.4219979565332407E-14,null,23950,4.4219979565332407E-14,""]
[{"$f":"\"P(\"&DOLLAR(B19,0)&B21&DOLLAR(B20,0)&\") = \"","v":"P($80,000 <= x <= $100,000) = "},{"$f":"_xlfn.NORM.DIST(B20,B17,B18,1)-_xlfn.NORM.DIST(B19,B17,B18,1)","v":0.5977410660361675},null,null,null,null,null,null,24000,1.1015763624682309E-12,"",null,24000,4.5590966468493575E-14,4.5590966468493575E-14,null,24000,4.5590966468493575E-14,""]
[null,null,null,null,null,null,null,null,24050,1.1345427550166375E-12,"",null,24050,4.7003393311255776E-14,4.7003393311255776E-14,null,24050,4.7003393311255776E-14,""]
["Frozen Corn Bag Filling Machine weight follows a normal distribution",null,null,null,null,null,null,null,24100,1.1684665063049869E-12,"",null,24100,4.8458478872809898E-14,4.8458478872809898E-14,null,24100,4.8458478872809898E-14,""]
["Mean weight of package",16,"oz.",null,null,null,null,null,24150,1.2033745206136439E-12,"",null,24150,4.9957476729542026E-14,4.9957476729542026E-14,null,24150,4.9957476729542026E-14,""]
["Sigma",0.3,"oz.",null,null,null,null,null,24200,1.239294431415013E-12,"",null,24200,5.150167621679003E-14,5.150167621679003E-14,null,24200,5.150167621679003E-14,""]
["What is probability of getting between +/- 1.96 Standard Deviations?",1.96,{"$f":"_xlfn.NORM.S.DIST(B27,1)-_xlfn.NORM.S.DIST(-B27,1)","v":0.95000420970355903},null,null,null,null,null,24250,1.2762546203536441E-12,"",null,24250,5.3092403416246521E-14,5.3092403416246521E-14,null,24250,5.3092403416246521E-14,""]
["What are the two x values of weight that bookend the +/- 1.96 Standard Deviations?",null,null,null,null,null,null,null,24300,1.3142842366982141E-12,"",null,24300,5.4731022169663593E-14,5.4731022169663593E-14,null,24300,5.4731022169663593E-14,""]
["Lower",{"$f":"B25-B26*B27","v":15.412000000000001},null,null,null,null,null,null,24350,1.353413217276506E-12,"",null,24350,5.6418935119531527E-14,5.6418935119531527E-14,null,24350,5.6418935119531527E-14,""]
["Upper",{"$f":"B25+B26*B27","v":16.588000000000001},null,null,null,null,null,null,24400,1.3936723069047391E-12,"",null,24400,5.8157584777422871E-14,5.8157584777422871E-14,null,24400,5.8157584777422871E-14,""]
["What is probability of getting between +/- 1.96 Standard Deviations?",{"$f":"_xlfn.NORM.DIST(B30,B25,B26,1)-_xlfn.NORM.DIST(B29,B25,B26,1)","v":0.95000420970355914},null,null,null,null,null,null,24450,1.435093079322912E-12,"",null,24450,5.9948454620704652E-14,5.9948454620704652E-14,null,24450,5.9948454620704652E-14,""]
["What is probability of NOT getting between +/- 1.96 Standard Deviations?",{"$f":"1-B31","v":4.9995790296440856E-2},null,{"$f":"1-(_xlfn.NORM.DIST(B30,B25,B26,1)-_xlfn.NORM.DIST(B29,B25,B26,1))","v":4.9995790296440856E-2},null,null,null,null,24500,1.4777079586480055E-12,"",null,24500,6.1793070218348656E-14,6.1793070218348656E-14,null,24500,6.1793070218348656E-14,""]
[null,null,null,null,null,null,null,null,24550,1.5215502413571453E-12,"",null,24550,6.3693000386572383E-14,6.3693000386572383E-14,null,24550,6.3693000386572383E-14,""]
["Nielsen Reports",null,null,null,null,null,null,null,24600,1.5666541188132573E-12,"",null,24600,6.564985837507706E-14,6.564985837507706E-14,null,24600,6.564985837507706E-14,""]
["Mean daily TV watched per household",8.4,"hours",null,null,null,null,null,24650,1.6130547003457386E-12,"",null,24650,6.7665303084654466E-14,6.7665303084654466E-14,null,24650,6.7665303084654466E-14,""]
[{"$f":"\"If distribution normal with SD of \"&B36&\" hours\"","v":"If distribution normal with SD of 2.5 hours"},2.5,"hours",null,null,null,null,null,24700,1.6607880368992045E-12,"",null,24700,6.9741040316965009E-14,6.9741040316965009E-14,null,24700,6.9741040316965009E-14,""]
[{"$f":"\"P(Hours Watched Per Day \"&D37&C37&\" hours) = \"","v":"P(Hours Watched Per Day >=10 hours) = "},{"$f":"1-_xlfn.NORM.DIST(C37,B35,B36,1)","v":0.26108629969286157},10,">=",null,null,null,null,24750,1.7098911452635135E-12,"",null,24750,7.1878824057295551E-14,7.1878824057295551E-14,null,24750,7.1878824057295551E-14,""]
[{"$f":"\"# Hours Watched per Day to be in lowest \"&TEXT(C38,\"0%\")","v":"# Hours Watched per Day to be in lowest 1%"},{"$f":"_xlfn.NORM.INV(C38,B35,B36)","v":2.584130314897898},0.01,null,null,null,null,null,24800,1.7604020328985782E-12,"",null,24800,7.4080457791139954E-14,7.4080457791139954E-14,null,24800,7.4080457791139954E-14,""]
[{"$f":"\"P(x\"&D39&C39&\") = \"","v":"P(x<=1) = "},{"$f":"_xlfn.NORM.DIST(C39,B35,B36,1)","v":1.538195211738057E-3},1,"<=",null,null,null,null,24850,1.8123597233678709E-12,"",null,24850,7.6347795855451327E-14,7.6347795855451327E-14,null,24850,7.6347795855451327E-14,""]
[null,null,null,null,null,null,null,null,24900,1.8658042823946179E-12,"",null,24900,7.8682744825446391E-14,7.8682744825446391E-14,null,24900,7.8682744825446391E-14,""]
[null,null,null,null,null,null,null,null,24950,1.9207768445551854E-12,"",null,24950,8.1087264937857317E-14,8.1087264937857317E-14,null,24950,8.1087264937857317E-14,""]
[null,null,null,null,null,null,null,null,25000,1.9773196406244673E-12,"",null,25000,8.3563371551552251E-14,8.3563371551552251E-14,null,25000,8.3563371551552251E-14,""]
[null,null,null,null,null,null,null,null,25050,2.0354760255882105E-12,"",null,25050,8.611313664646052E-14,8.611313664646052E-14,null,25050,8.611313664646052E-14,""]
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[null,null,null,null,null,null,null,null,25150,2.1568087760625944E-12,"",null,25150,9.1442222574403202E-14,9.1442222574403202E-14,null,25150,9.1442222574403202E-14,""]
[null,null,null,null,null,null,null,null,25200,2.220077734357901E-12,"",null,25200,9.4225984518704151E-14,9.4225984518704151E-14,null,25200,9.4225984518704151E-14,""]
[null,null,null,null,null,null,null,null,25250,2.2851455280615134E-12,"",null,25250,9.7092290448508872E-14,9.7092290448508872E-14,null,25250,9.7092290448508872E-14,""]
[null,null,null,null,null,null,null,null,25300,2.3520615778390839E-12,"",null,25300,1.0004351934251745E-13,1.0004351934251745E-13,null,25300,1.0004351934251745E-13,""]
[null,null,null,null,null,null,null,null,25350,2.4208766115332881E-12,"",null,25350,1.0308211665413795E-13,1.0308211665413795E-13,null,25350,1.0308211665413795E-13,""]
[null,null,null,null,null,null,null,null,25400,2.4916426972950988E-12,"",null,25400,1.0621059610688366E-13,1.0621059610688366E-13,null,25400,1.0621059610688366E-13,""]
[null,null,null,null,null,null,null,null,25450,2.5644132775147113E-12,"",null,25450,1.0943154153646636E-13,1.0943154153646636E-13,null,25450,1.0943154153646636E-13,""]
[null,null,null,null,null,null,null,null,25500,2.6392432035705738E-12,"",null,25500,1.1274760878074369E-13,1.1274760878074369E-13,null,25500,1.1274760878074369E-13,""]
[null,null,null,null,null,null,null,null,25550,2.7161887714150017E-12,"",null,25550,1.1616152761872172E-13,1.1616152761872172E-13,null,25550,1.1616152761872172E-13,""]
[null,null,null,null,null,null,null,null,25600,2.795307758015465E-12,"",null,25600,1.1967610375982232E-13,1.1967610375982232E-13,null,25600,1.1967610375982232E-13,""]
[null,null,null,null,null,null,null,null,25650,2.8766594586709027E-12,"",null,25650,1.2329422088467054E-13,1.2329422088467054E-13,null,25650,1.2329422088467054E-13,""]
[null,null,null,null,null,null,null,null,25700,2.9603047252230049E-12,"",null,25700,1.2701884273867766E-13,1.2701884273867766E-13,null,25700,1.2701884273867766E-13,""]
[null,null,null,null,null,null,null,null,25750,3.0463060051826217E-12,"",null,25750,1.3085301527972812E-13,1.3085301527972812E-13,null,25750,1.3085301527972812E-13,""]
[null,null,null,null,null,null,null,null,25800,3.1347273817919788E-12,"",null,25800,1.3479986888131017E-13,1.3479986888131017E-13,null,25800,1.3479986888131017E-13,""]
[null,null,null,null,null,null,null,null,25850,3.2256346150438975E-12,"",null,25850,1.3886262059245959E-13,1.3886262059245959E-13,null,25850,1.3886262059245959E-13,""]
[null,null,null,null,null,null,null,null,25900,3.3190951836795374E-12,"",null,25900,1.4304457645592316E-13,1.4304457645592316E-13,null,25900,1.4304457645592316E-13,""]
[null,null,null,null,null,null,null,null,25950,3.4151783281865774E-12,"",null,25950,1.473491338859688E-13,1.473491338859688E-13,null,25950,1.473491338859688E-13,""]
[null,null,null,null,null,null,null,null,26000,3.5139550948204338E-12,"",null,26000,1.5177978410732545E-13,1.5177978410732545E-13,null,26000,1.5177978410732545E-13,""]
[null,null,null,null,null,null,null,null,26050,3.6154983806715053E-12,"",null,26050,1.5634011465674277E-13,1.5634011465674277E-13,null,26050,1.5634011465674277E-13,""]
[null,null,null,null,null,null,null,null,26100,3.7198829798016039E-12,"",null,26100,1.6103381194871936E-13,1.6103381194871936E-13,null,26100,1.6103381194871936E-13,""]
[null,null,null,null,null,null,null,null,26150,3.8271856304738066E-12,"",null,26150,1.6586466390697023E-13,1.6586466390697023E-13,null,26150,1.6586466390697023E-13,""]
[null,null,null,null,null,null,null,null,26200,3.9374850634998497E-12,"",null,26200,1.7083656266324566E-13,1.7083656266324566E-13,null,26200,1.7083656266324566E-13,""]
[null,null,null,null,null,null,null,null,26250,{"$f":"_xlfn.NORM.DIST(I67,$B$3,$B$4,0)","v":4.0508620517302679E-12},{"$f":"IF(I67>=$B$5,J67,\"\")","v":""},null,26250,{"$f":"_xlfn.NORM.DIST(M67,$B$10,$B$11,0)","v":1.7595350732515519E-13},{"$f":"IF(M67<=$B$12,N67,\"\")","v":1.7595350732515519E-13},null,26250,{"$f":"_xlfn.NORM.DIST(Q67,$B$10,$B$11,0)","v":1.7595350732515519E-13},{"$f":"IF(AND(Q67>=$B$19,Q67<=$B$20),R67,\"\")","v":""}]
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[null,null,null,null,null,null,null,null,26350,4.2871823005422226E-12,"",null,26350,1.8663908277907179E-13,1.8663908277907179E-13,null,26350,1.8663908277907179E-13,""]
[null,null,null,null,null,null,null,null,26400,4.4102977789373076E-12,"",null,26400,1.9221627257602341E-13,1.9221627257602341E-13,null,26400,1.9221627257602341E-13,""]
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[null,null,null,null,null,null,null,null,26500,4.6668867975942561E-12,"",null,26500,2.0386174009475572E-13,2.0386174009475572E-13,null,26500,2.0386174009475572E-13,""]
[null,null,null,null,null,null,null,null,26550,4.800546236680796E-12,"",null,26550,2.0993929902491636E-13,2.0993929902491636E-13,null,26550,2.0993929902491636E-13,""]
[null,null,null,null,null,null,null,null,26600,4.9379102271104488E-12,"",null,26600,2.1619314072341274E-13,2.1619314072341274E-13,null,26600,2.1619314072341274E-13,""]
[null,null,null,null,null,null,null,null,26650,5.0790778054342375E-12,"",null,26650,2.2262822860193745E-13,2.2262822860193745E-13,null,26650,2.2262822860193745E-13,""]
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[null,null,null,null,null,null,null,null,26750,5.3732326505691496E-12,"",null,26750,2.3606267651897738E-13,2.3606267651897738E-13,null,26750,2.3606267651897738E-13,""]
[null,null,null,null,null,null,null,null,26800,5.5264309577497159E-12,"",null,26800,2.4307265411616878E-13,2.4307265411616878E-13,null,26800,2.4307265411616878E-13,""]
[null,null,null,null,null,null,null,null,26850,5.6838550627628879E-12,"",null,26850,2.5028512039737674E-13,2.5028512039737674E-13,null,26850,2.5028512039737674E-13,""]
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[null,null,null,null,null,null,null,null,27150,6.7236402433581379E-12,"",null,27150,2.9814106172283947E-13,2.9814106172283947E-13,null,27150,2.9814106172283947E-13,""]
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{"sheet":"D","index":23,"n_rows":703,"n_cols":5,"rows_kept":703,"cut":false,"hidden":false,"merged":[]}
["For a particular Disney Ride, the mean time to wait in line is 22 minutes (Distribution follows an Exponential Distribution pattern)."]
["mu",22,"time to stand in line"]
["x",15]
[{"$f":"\"P(x<=\"&$B$3&\")\"","v":"P(x<=15)"},null,"."]
[{"$f":"\"P(x<=\"&$B$3&\")\"","v":"P(x<=15)"},null,null," =EXPON.DIST(B3,1/B2,1)"]
["x",25]
[{"$f":"\"P(x>=\"&$B$6&\")\"","v":"P(x>=25)"},null,"."]
[{"$f":"\"P(x>=\"&$B$6&\")\"","v":"P(x>=25)"},null,null," =1-EXPON.DIST(B6,1/B2,1)"]
[{"$f":"\"P(\"&$B$3&\"<=x<=\"&$B$6&\")\"","v":"P(15<=x<=25)"},null,"."]
[{"$f":"\"P(\"&$B$3&\"<=x<=\"&$B$6&\")\"","v":"P(15<=x<=25)"},null,null," =EXPON.DIST(B6,1/B2,1)-EXPON.DIST(B3,1/B2,1)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["x","f(x)",{"$f":"A4","v":"P(x<=15)"},{"$f":"A7","v":"P(x>=25)"},{"$f":"A10","v":"P(15<=x<=25)"}]
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{"sheet":"D (an)","index":24,"n_rows":703,"n_cols":5,"rows_kept":703,"cut":false,"hidden":false,"merged":[]}
["For a particular Disney Ride, the mean time to wait in line is 22 minutes (Distribution follows an Exponential Distribution pattern."]
["mu",22,"time to stand in line"]
["x",15]
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["x",25]
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[]
[]
[]
[]
[]
[]
[]
[]
[]
["x","f(x)",{"$f":"A4","v":"P(x<=15)"},{"$f":"A7","v":"P(x>=25)"},{"$f":"A10","v":"P(15<=x<=25)"}]
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{"sheet":"Sheet5","index":25,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Sheet8","index":26,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Sheet7","index":27,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Sheet6","index":28,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"Exp","index":29,"n_rows":528,"n_cols":9,"rows_kept":528,"cut":false,"hidden":true,"merged":[]}
["Exponential Probability Distribution"]
["Continuous Random Variable"]
["X > = 0"]
["Mean = Standard Deviation"]
["Excel function: EXPON.DIST"]
["EXPON.DIST(x,1/mu, (0 = exact, 1 = cumulative))",null,null,null,null,"or cumulative function = 1 - e^(-x/mu)"]
[]
["According to a recent study, business people are interrupted 5.5 times per hour. Assume that the distribution follows an Exponential Distribution"]
[{"$f":"\"Mean for Poisson Distribution = \"&B10&\" = \"&C10&\" \"&D10&\" \"&E10&\" \"&F10","v":"Mean for Poisson Distribution = # interruptions = 5.5 per 1 hour"}]
["x","# interruptions",5.5,"per",1,"hour"]
[null,null,null,null,60,"minutes"]
[{"$f":"\"Mean for Exponetial Distribution = \"&B13&\" = \"&C13&\" \"&D13&\" \"&E13&\" \"&F13","v":"Mean for Exponetial Distribution = x = Time between interruptions = 0.181818181818182 hours  "}]
["x","x = Time between interruptions",{"$f":"E10/C10","v":0.18181818181818182},"hours"]
[null,null,{"$f":"C13*60","v":10.90909090909091},"minutes"]
[]
["P(get interrupted in the next 10 minutes)"]
[null,null,"x1","x2"]
[null,null,0,10,"minutes"]
[null,{"$f":"\"P(x<\"&$D$23&\")\"","v":"P(x<15)"},{"$f":"_xlfn.EXPON.DIST(D18,1/$C$14,1)","v":0.60015034565515268},null," =EXPON.DIST(D18,1/$C$14,1)"]
[null,{"$f":"\"P(x<\"&$D$23&\")\"","v":"P(x<15)"},{"$f":"1-EXP(1)^(-D18/$C$14)","v":0.60015034565515268},null," =1-EXP(1)^(-D18/$C$14)",null,null,null,"1 - e^(-x/mu)"]
["P(not interruptions during 15 minute)"]
[null,null,"x1","x2"]
[null,null,0,15,"minutes"]
[null,{"$f":"\"P(x>\"&$D$23&\")\"","v":"P(x>15)"},{"$f":"1-_xlfn.EXPON.DIST(D23,1/$C$14,1)","v":0.25283959580474646},null," =1-EXPON.DIST(D23,1/$C$14,1)"]
[null,{"$f":"\"P(x>\"&$D$23&\")\"","v":"P(x>15)"},{"$f":"EXP(1)^(-D23/$C$14)","v":0.25283959580474652},null," =EXP(1)^(-D23/$C$14)"]
[]
["x (min)","f(x)",{"$f":"\"P(x<\"&D18&\") = \"&TEXT(EXPONDIST(D18,1/$C$14,1),\"0.0000\")","v":"P(x<10) = 0.6002"},{"$f":"\"P(x>\"&D23&\") = \"&TEXT(1-EXPONDIST(D23,1/$C$14,1),\"0.00%\")","v":"P(x>15) = 25.28%"},"."]
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[46.600000000000392,1.2795291290627017E-3,"",1.2795291290627017E-3]
[46.700000000000394,1.2678537061561535E-3,"",1.2678537061561535E-3]
[46.800000000000395,1.2562848189250752E-3,"",1.2562848189250752E-3]
[46.900000000000396,1.2448214952547724E-3,"",1.2448214952547724E-3]
[47.000000000000398,1.2334627719008881E-3,"",1.2334627719008881E-3]
[47.100000000000399,1.2222076944084551E-3,"",1.2222076944084551E-3]
[47.200000000000401,1.2110553170317016E-3,"",1.2110553170317016E-3]
[47.300000000000402,1.200004702654579E-3,"",1.200004702654579E-3]
[47.400000000000404,1.1890549227120137E-3,"",1.1890549227120137E-3]
[47.500000000000405,1.1782050571118893E-3,"",1.1782050571118893E-3]
[47.600000000000406,1.1674541941577247E-3,"",1.1674541941577247E-3]
[47.700000000000408,1.1568014304720723E-3,"",1.1568014304720723E-3]
[47.800000000000409,1.1462458709206027E-3,"",1.1462458709206027E-3]
[47.900000000000411,1.135786628536895E-3,"",1.135786628536895E-3]
[48.000000000000412,1.1254228244478978E-3,"",1.1254228244478978E-3]
[48.100000000000414,1.115153587800089E-3,"",1.115153587800089E-3]
[48.200000000000415,1.1049780556862886E-3,"",1.1049780556862886E-3]
[48.300000000000416,1.0948953730731605E-3,"",1.0948953730731605E-3]
[48.400000000000418,1.0849046927293561E-3,"",1.0849046927293561E-3]
[48.500000000000419,1.0750051751543309E-3,"",1.0750051751543309E-3]
[48.600000000000421,1.0651959885077957E-3,"",1.0651959885077957E-3]
[48.700000000000422,1.055476308539824E-3,"",1.055476308539824E-3]
[48.800000000000423,1.0458453185215892E-3,"",1.0458453185215892E-3]
[48.900000000000425,1.0363022091767337E-3,"",1.0363022091767337E-3]
[49.000000000000426,1.0268461786133729E-3,"",1.0268461786133729E-3]
[49.100000000000428,1.0174764322567064E-3,"",1.0174764322567064E-3]
[49.200000000000429,1.0081921827822578E-3,"",1.0081921827822578E-3]
[49.300000000000431,9.9899265004971174E-4,"",9.9899265004971174E-4]
[49.400000000000432,9.898770610373643E-4,"",9.898770610373643E-4]
[49.500000000000433,9.8084464977716244E-4,"",9.8084464977716244E-4]
[49.600000000000435,9.7189465729034721E-4,"",9.7189465729034721E-4]
[49.700000000000436,9.63026331523671E-4,"",9.63026331523671E-4]
[49.800000000000438,9.5423892728621065E-4,"",9.5423892728621065E-4]
[49.900000000000439,9.4553170618674374E-4,"",9.4553170618674374E-4]
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{"sheet":"Ex v Po","index":30,"n_rows":17,"n_cols":18,"rows_kept":17,"cut":false,"hidden":true,"merged":[]}
["Relationship between Poisson and Exponential\nPoisson is # of occurrences during per Interval\nExponential is length between occurrences\nIf occurrences follow a Poisson Distr., the length between occurrences must follow an Exponential Distribution",null,null,null,null,null,null,null,null,null,null,null,"Poisson Probability Distribution can be used to estimate the number of occurrences over a specified interval of time or space",null,null,null,null,"Exponential Probability Distribution can be used to estimate the length of the interval between occurrences (time or space)"]
[{"$f":"\"Mean for Poisson Distribution = \"&B3&\" = \"&C3&\" \"&D3&\" \"&E3&\" \"&F3","v":"Mean for Poisson Distribution = # interruptions = 5.5 per 1 hour"},null,null,null,null,null,null,null,null,null,null,null,"Discrete Random Variable",null,null,null,null,"Continuous Random Variable"]
["x","# interruptions",{"$f":"Exp!C10","v":5.5},"per",1,"hour",null,null,null,null,null,null,"Properties of a Poisson Experiment:",null,null,null,null,"X > = 0"]
[null,null,null,null,60,"minutes",null,null,null,null,null,null,"The probability of an occurrence is the same for any two intervals of equal length",null,null,null,null,"Mean = Standard Deviation"]
[{"$f":"\"Mean for Exponetial Distribution = \"&B6&\" = \"&C6&\" \"&D6&\" \"&E6&\" \"&F6","v":"Mean for Exponetial Distribution = Time between interruptions = 0.181818181818182 hours  "},null,null,null,null,null,null,null,null,null,null,null,"The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval",null,null,null,null,"Excel function: EXPON.DIST"]
["x","Time between interruptions",{"$f":"E3/C3","v":0.18181818181818182},"hours",null,null,null,null,null,null,null,null,"No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gets quite small.",null,null,null,null,"EXPON.DIST(x,1/mu, (0 = exact, 1 = cumulative))"]
[null,null,{"$f":"C6*E4","v":10.90909090909091},"minutes",null,null,null,null,null,null,null,null,"Mean = Var"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Excel function: POISSON.DIST"]
["P(no interruptions during 15 minute period 0 to 15)",null,null,null,null,null,null,null,null,null,null,null,"POISSON.DIST(x,mean,cumulative (0 = exact, 1 = cumulative))"]
[null,null,"x1","x2"]
[null,null,0,15,"minutes"]
[null,"P(X>15)",{"$f":"1-_xlfn.EXPON.DIST(D11,1/C7,1)","v":0.25283959580474646},"Exponential, x = time between occurrences",null,null,null,null," =1-EXPON.DIST(D12,1/C7,1)"]
[]
[null,"x =",0,"# of occurrences"]
[null,"Time ="]
[null,{"$f":"\"Mean = # occurrences per \"&D11&\" \"&E11","v":"Mean = # occurrences per 15 minutes"}]
[null,{"$f":"\"P(x<\"&C14&\")\"","v":"P(x<0)"},null,"Poisson, x = # of occurrences",null,null,null,null," =POISSON.DIST(C15,C17,0)"]

{"sheet":"Ex v Po (an)","index":31,"n_rows":18,"n_cols":18,"rows_kept":18,"cut":false,"hidden":true,"merged":[]}
["Relationship between Poisson and Exponential\nPoisson is # of occurrences during per Interval\nExponential is length between occurrences\nIf occurrences follow a Poisson Distr., the length between occurrences must follow an Exponential Distribution",null,null,null,null,null,null,null,null,null,null,null,"Poisson Probability Distribution can be used to estimate the number of occurrences over a specified interval of time or space",null,null,null,null,"Exponential Probability Distribution can be used to estimate the length of the interval between occurrences (time or space)"]
[{"$f":"\"Mean for Poisson Distribution = \"&B3&\" = \"&C3&\" \"&D3&\" \"&E3&\" \"&F3","v":"Mean for Poisson Distribution = # interruptions = 5.5 per 1 hour"},null,null,null,null,null,null,null,null,null,null,null,"Discrete Random Variable",null,null,null,null,"Continuous Random Variable"]
["x","# interruptions",{"$f":"Exp!C10","v":5.5},"per",1,"hour",null,null,null,null,null,null,"Properties of a Poisson Experiment:",null,null,null,null,"X > = 0"]
[null,null,null,null,60,"minutes",null,null,null,null,null,null,"The probability of an occurrence is the same for any two intervals of equal length",null,null,null,null,"Mean = Standard Deviation"]
[{"$f":"\"Mean for Exponetial Distribution = \"&B6&\" = \"&C6&\" \"&D6&\" \"&E6&\" \"&F6","v":"Mean for Exponetial Distribution = Time between interruptions = 0.181818181818182 hours  "},null,null,null,null,null,null,null,null,null,null,null,"The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval",null,null,null,null,"Excel function: EXPON.DIST"]
["x","Time between interruptions",{"$f":"E3/C3","v":0.18181818181818182},"hours",null,null,null,null,null,null,null,null,"No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gets quite small.",null,null,null,null,"EXPON.DIST(x,1/mu, (0 = exact, 1 = cumulative))"]
[null,null,{"$f":"E4/C3","v":10.909090909090908},"minutes",null,null,null,null,null,null,null,null,"Mean = Var"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Excel function: POISSON.DIST"]
["P(no interruptions during 15 minute period 0 to 15)",null,null,null,null,null,null,null,null,null,null,null,"POISSON.DIST(x,mean,cumulative (0 = exact, 1 = cumulative))"]
[]
[null,null,"x1","x2"]
[null,null,0,15,"minutes"]
[null,"P(X>15)",{"$f":"1-_xlfn.EXPON.DIST(D12,1/C7,1)","v":0.25283959580474646},"Exponential, x = time between occurrences",null,null,null,null," =1-EXPON.DIST(D12,1/C7,1)"]
[]
[null,"x =",0,"# of occurrences"]
[null,"Time =",{"$f":"D12/E4","v":0.25}]
[null,{"$f":"\"Mean = # occurrences per \"&D12&\" \"&E12","v":"Mean = # occurrences per 15 minutes"},{"$f":"C16*C3","v":1.375}]
[null,{"$f":"\"P(x<\"&C15&\")\"","v":"P(x<0)"},{"$f":"_xlfn.POISSON.DIST(C15,C17,1)","v":0.25283959580474646},"Poisson, x = # of occurrences",null,null,null,null," =POISSON.DIST(C15,C17,0)"]