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{"sheet":"Topics","index":0,"n_rows":11,"n_cols":1,"rows_kept":11,"cut":false,"hidden":false,"merged":[]}
["Random Variables"]
["Discrete Random Variables"]
["Continuous Random Variables"]
["Discrete Probability Distributions"]
["Expected Value for a  Discrete Random Variables"]
["Variance and Standard Deviation for a Discrete Random Variables"]
["Binomial Experiment"]
["Binomial Probabilities"]
["Expected Value and Variance and Standard Deviation for a Binomial Distribution"]
["POISSON Distibution"]
["Hypergeometric Distribution"]

{"sheet":"PD(1)","index":1,"n_rows":34,"n_cols":7,"rows_kept":34,"cut":false,"hidden":false,"merged":[]}
["Experiment of tossing coin three times"]
["Steps in Experiment",3]
["Outcomes Step 1",2]
["Outcomes Step 2",2]
["Outcomes Step 3",2,null,null,null,"Success ="]
["Total Experimental Outcomes",{"$f":"PRODUCT(B3:B5)","v":8},"(Sample Points)",null,null,"Heads"]
["P(for each) =",{"$f":"1/B6","v":0.125},"Classical",null,null,{"$f":"\"Notation for \"&F6&\" is \"&LEFT(F6,1)","v":"Notation for Heads is H"}]
[null,null,null,null,null,{"$f":"LEFT(F6,1)","v":"H"}]
["# SP","Toss 1","Toss 2","Toss 3","Sample Space","Probability of Sample Point","# of heads for sample points"]
[1,"H","H","H",{"$f":"\"(\"&B10&\", \"&C10&\", \"&D10&\")\"","v":"(H, H, H)"},{"$f":"1/$B$6","v":0.125},{"$f":"COUNTIF(B10:D10,$F$8)","v":3}]
[2,"T","H","H",{"$f":"\"(\"&B11&\", \"&C11&\", \"&D11&\")\"","v":"(T, H, H)"},0.125,2]
[3,"H","T","H","(H, T, H)",0.125,2]
[4,"H","H","T","(H, H, T)",0.125,2]
[5,"T","T","H","(T, T, H)",0.125,1]
[6,"T","H","T","(T, H, T)",0.125,1]
[7,"H","T","T","(H, T, T)",0.125,1]
[8,"T","T","T","(T, T, T)",0.125,0]
[null,null,null,null,null,{"$f":"SUM(F10:F17)","v":1}]
["x = Discrete Random Variable =","# of heads in 3 flips"]
[null,null,null,null,"Steps:","#1","Define Random Variable"]
["X","Frequency","P(X) = f(x)","Each f(x)>=0?",null,"#2","Build Frequency Distribution"]
[0,{"$f":"COUNTIF($G$10:$G$17,A22)","v":1},{"$f":"B22/$B$26","v":0.125},{"$f":"C22>=0","v":true},null,"#3","Calculate Relative Frequency - P(x) = f(x)"]
[1,{"$f":"COUNTIF($G$10:$G$17,A23)","v":3},{"$f":"B23/$B$26","v":0.375},{"$f":"C23>=0","v":true},null,"#4","Check Requirement #1: f(x) >= 0"]
[2,{"$f":"COUNTIF($G$10:$G$17,A24)","v":3},{"$f":"B24/$B$26","v":0.375},{"$f":"C24>=0","v":true},null,"#5","Check Requirement #2: Σf(x) = 1"]
[3,{"$f":"COUNTIF($G$10:$G$17,A25)","v":1},{"$f":"B25/$B$26","v":0.125},{"$f":"C25>=0","v":true},null,"#6","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
[null,{"$f":"SUM(B22:B25)","v":8},{"$f":"SUM(C22:C25)","v":1},null,null,"#7","Make predictions"]
[]
["P(X =1)"]
["P(X > = 2)"]
["P(x = 0 or x = 3)",null,{"$f":"C22+C25","v":0.25}]
["P(X not 2)",null,{"$f":"1-C24","v":0.625}]
[]
[]
["."]

{"sheet":"PD(1)an","index":2,"n_rows":31,"n_cols":7,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["Experiment of tossing coin three times"]
["Steps in Experiment",3]
["Outcomes Step 1",2]
["Outcomes Step 2",2]
["Outcomes Step 3",2,null,null,null,"Success ="]
["Total Experimental Outcomes",{"$f":"PRODUCT(B3:B5)","v":8},"(Sample Points)",null,null,"Heads"]
["P(for each) =",{"$f":"1/B6","v":0.125},"Classical",null,null,{"$f":"\"Notation for \"&F6&\" is \"&LEFT(F6,1)","v":"Notation for Heads is H"}]
[null,null,null,null,null,{"$f":"LEFT(F6,1)","v":"H"}]
["# SP","Toss 1","Toss 2","Toss 3","Sample Space","Probability of Sample Point","# of heads for sample points"]
[1,"H","H","H",{"$f":"\"(\"&B10&\", \"&C10&\", \"&D10&\")\"","v":"(H, H, H)"},{"$f":"1/$B$6","v":0.125},{"$f":"COUNTIF(B10:D10,$F$8)","v":3}]
[2,"T","H","H",{"$f":"\"(\"&B11&\", \"&C11&\", \"&D11&\")\"","v":"(T, H, H)"},0.125,2]
[3,"H","T","H","(H, T, H)",0.125,2]
[4,"H","H","T","(H, H, T)",0.125,2]
[5,"T","T","H","(T, T, H)",0.125,1]
[6,"T","H","T","(T, H, T)",0.125,1]
[7,"H","T","T","(H, T, T)",0.125,1]
[8,"T","T","T","(T, T, T)",0.125,0]
[null,null,null,null,null,{"$f":"SUM(F10:F17)","v":1}]
["x = Discrete Random Variable =","# of heads in 3 flips"]
[null,null,null,null,"Steps:","#1","Define Random Variable"]
["X","Frequency","P(X) = f(x)","Each f(x)>=0?",null,"#2","Build Frequency Distribution"]
[0,{"$f":"COUNTIF($G$10:$G$17,A22)","v":1},{"$f":"B22/$B$26","v":0.125},{"$f":"C22>=0","v":true},null,"#3","Calculate Relative Frequency - P(x) = f(x)"]
[1,{"$f":"COUNTIF($G$10:$G$17,A23)","v":3},{"$f":"B23/$B$26","v":0.375},{"$f":"C23>=0","v":true},null,"#4","Check Requirement #1: f(x) >= 0"]
[2,{"$f":"COUNTIF($G$10:$G$17,A24)","v":3},{"$f":"B24/$B$26","v":0.375},{"$f":"C24>=0","v":true},null,"#5","Check Requirement #2: Σf(x) = 1"]
[3,{"$f":"COUNTIF($G$10:$G$17,A25)","v":1},{"$f":"B25/$B$26","v":0.125},{"$f":"C25>=0","v":true},null,"#6","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
[null,{"$f":"SUM(B22:B25)","v":8},{"$f":"SUM(C22:C25)","v":1},null,null,"#7","Make predictions"]
[]
["P(X =1)",{"$f":"C22","v":0.125}]
["P(X > = 2)",{"$f":"SUM(C24:C25)","v":0.5}]
["P(x = 0 or x = 3)",{"$f":"SUM(C22,C25)","v":0.25},{"$f":"C22+C25","v":0.25}]
["P(X not 2)",{"$f":"SUM(C22:C23,C25)","v":0.625},{"$f":"1-C24","v":0.625}]

{"sheet":"PD(2)","index":3,"n_rows":24,"n_cols":10,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
["Over last 20 days the number of operating rooms used at TG hospital were:",null,null,null,"Steps to Build Discrete Probability Distribution:"]
["On 3 days only 1 were used",null,null,null,"#1","Define Random Variable"]
["On 5 days 2 were used",null,null,null,"#2","Build Frequency Distribution"]
["On 8 days 3 were used",null,null,null,"#3","Calculate Relative Frequency - P(x) = f(x)"]
["On 4 days all (4) were used",null,null,null,"#4","Check Requirement #1: f(x) >= 0"]
["Create a Probability Distribution that can be used to make predictions in the future.",null,null,null,"#5","Check Requirement #2: Σf(x) = 1"]
[null,null,null,null,"#6","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
["Discrete Random Variable = x =","# of operating rooms used in 1 day",null,null,"#7","Make predictions"]
[]
["Frequency (# of days)","x = # operating rooms in use for 1 day","Relative Frequency P(x) = f(x) = Probability","Is each f(x) >= 0?","P(x)","f(x)"]
[3,1,null,null,{"$f":"LEFT(E$10,1)&\"(\"&$B11&\")\"","v":"P(1)"},"f(1)"]
[5,2,null,null,"P(2)","f(2)"]
[8,3,null,null,"P(3)","f(3)"]
[4,4,null,null,"P(4)","f(4)"]
[]
[null,null,null,null,null,null,null,null,null,"Discrete Probability Charts don't have columns that touch."]
["Reason we do the whole distribution? Because then it is easy to make predictions"]
[null,null,null,null,null,null,"check"]
[2,{"$f":"\"<=\"&A19","v":"<=2"},{"$f":"\"P(x\"&B19&\")\"","v":"P(x<=2)"},"f(1) + f(2)",null,null,null,null,"SUMIF function:"]
[2,{"$f":"\"<\"&A20","v":"<2"},{"$f":"\"P(x\"&B20&\")\"","v":"P(x<2)"},"f(1)",null,null,null,null,"range = range with all criteria"]
[2,{"$f":"\">=\"&A21","v":">=2"},{"$f":"\"P(x\"&B21&\")\"","v":"P(x>=2)"},"f(2) + f(3) + f(4)",null,null,null,null,"criteria = criteria such as 2, <=2, >=2, >2"]
[2,{"$f":"\">\"&A22","v":">2"},{"$f":"\"P(x\"&B22&\")\"","v":"P(x>2)"},"f(3) + f(4)",null,null,null,null,"sum_range = range with values to add"]
[null,null,null,null,null,null,null,null,"For more about this function, see this video:"]
[null,null,null,null,null,null,null,null,"Excel Magic Trick #203: SUMIF function formula 21 Examples"]

{"sheet":"PD(2)an","index":4,"n_rows":24,"n_cols":10,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
["Over last 20 days the number of operating rooms used at TG hospital were:",null,null,null,"Steps to Build Discrete Probability Distribution:"]
["On 3 days only 1 were used",null,null,null,"#1","Define Random Variable"]
["On 5 days 2 were used",null,null,null,"#2","Build Frequency Distribution"]
["On 8 days 3 were used",null,null,null,"#3","Calculate Relative Frequency - P(x) = f(x)"]
["On 4 days all (4) were used",null,null,null,"#4","Check Requirement #1: f(x) >= 0"]
["Create a Probability Distribution that can be used to make predictions in the future.",null,null,null,"#5","Check Requirement #2: Σf(x) = 1"]
[null,null,null,null,"#6","Create a Column Chart for a Discrete Variable (Columns do not touch)"]
["Discrete Random Variable = x =","X = # of Op. Rooms used in 1 day",null,null,"#7","Make predictions"]
[]
["Frequency (# of days)","x = # operating rooms in use for 1 day","Relative Frequency P(x) = f(x) = Probability","Is each f(x) >= 0?","P(x)","f(x)"]
[3,1,{"$f":"A11/$A$15","v":0.15},{"$f":"C11>=0","v":true},{"$f":"LEFT(E$10,1)&\"(\"&$B11&\")\"","v":"P(1)"},"f(1)"]
[5,2,{"$f":"A12/$A$15","v":0.25},{"$f":"C12>=0","v":true},"P(2)","f(2)"]
[8,3,{"$f":"A13/$A$15","v":0.4},{"$f":"C13>=0","v":true},"P(3)","f(3)"]
[4,4,{"$f":"A14/$A$15","v":0.2},{"$f":"C14>=0","v":true},"P(4)","f(4)"]
[{"$f":"SUM(A11:A14)","v":20},null,{"$f":"SUM(C11:C14)","v":1}]
[null,null,null,null,null,null,null,null,null,"Discrete Probability Charts don't have columns that touch."]
["Reason we do the whole distribution? Because then it is easy to make predictions"]
[null,null,null,null,null,null,"check"]
[2,{"$f":"\"<=\"&A19","v":"<=2"},{"$f":"\"P(x\"&B19&\")\"","v":"P(x<=2)"},"f(1) + f(2)",{"$f":"SUM(C11:C12)","v":0.4},null,{"$f":"SUMIF($B$11:$B$14,B19,$C$11:$C$14)","v":0.4},null,"SUMIF function:"]
[2,{"$f":"\"<\"&A20","v":"<2"},{"$f":"\"P(x\"&B20&\")\"","v":"P(x<2)"},"f(1)",{"$f":"SUM(C11)","v":0.15},null,{"$f":"SUMIF($B$11:$B$14,B20,$C$11:$C$14)","v":0.15},null,"range = range with all criteria"]
[2,{"$f":"\">=\"&A21","v":">=2"},{"$f":"\"P(x\"&B21&\")\"","v":"P(x>=2)"},"f(2) + f(3) + f(4)",{"$f":"SUM(C12:C14)","v":0.85000000000000009},null,{"$f":"SUMIF($B$11:$B$14,B21,$C$11:$C$14)","v":0.85000000000000009},null,"criteria = criteria such as 2, <=2, >=2, >2"]
[2,{"$f":"\">\"&A22","v":">2"},{"$f":"\"P(x\"&B22&\")\"","v":"P(x>2)"},"f(3) + f(4)",{"$f":"SUM(C13:C14)","v":0.60000000000000009},null,{"$f":"SUMIF($B$11:$B$14,B22,$C$11:$C$14)","v":0.60000000000000009},null,"sum_range = range with values to add"]
[null,null,null,null,null,null,null,null,"For more about this function, see this video:"]
[null,null,null,null,null,null,null,null,"Excel Magic Trick #203: SUMIF function formula 21 Examples"]

{"sheet":"PD(3)","index":5,"n_rows":6,"n_cols":5,"rows_kept":6,"cut":false,"hidden":false,"merged":[]}
["Job satisfaction score","IS Senior Executives","Is each f(x) >= 0?","IS Middle Executives","Is each f(x) >= 0?"]
[1,0.05,null,0.04]
[2,0.09,null,0.1]
[3,0.03,null,0.12]
[4,0.42,null,0.46]
[5,0.41,null,0.28000000000000003]

{"sheet":"PD(3)an","index":6,"n_rows":7,"n_cols":5,"rows_kept":7,"cut":false,"hidden":false,"merged":[]}
["Job satisfaction score","IS Senior Executives","Is each f(x) >= 0?","IS Middle Executives","Is each f(x) >= 0?"]
[1,0.05,{"$f":"B2>=0","v":true},0.04,true]
[2,0.09,true,0.1,true]
[3,0.03,true,0.12,true]
[4,0.42,true,0.46,true]
[5,0.41,true,0.28000000000000003,true]
[null,{"$f":"SUM(B2:B6)","v":1},null,{"$f":"SUM(D2:D6)","v":1}]

{"sheet":"EVSD(1)","index":7,"n_rows":30,"n_cols":11,"rows_kept":30,"cut":false,"hidden":false,"merged":[[7,8,10,8]]}
["Mean and Standard Deviation from Raw Data",null,null,null,"Mean and Standard Deviation for Discrete Probability Distribution"]
[null,null,null,null,"x = # operating rooms in use for 1 day","Frequency (# of days)","Relative Frequency P(x) = f(x) = Probability","E(x) =X*f(x)","X - mu","(X-mu)^2",{"$f":"J2&\"*f(x)\"","v":"(X-mu)^2*f(x)"}]
["Mean",null,null,null,1,{"$f":"COUNTIF($A$7:$A$26,E3)","v":3},{"$f":"F3/$F$7","v":0.15}]
["STDEV.S",null,null,null,2,{"$f":"COUNTIF($A$7:$A$26,E4)","v":5},{"$f":"F4/$F$7","v":0.25}]
["STDEV.P",null,null,null,3,{"$f":"COUNTIF($A$7:$A$26,E5)","v":8},{"$f":"F5/$F$7","v":0.4}]
["Raw Data = Xi","X - mu","(X-mu)^2",null,4,{"$f":"COUNTIF($A$7:$A$26,E6)","v":4},{"$f":"F6/$F$7","v":0.2}]
[1,null,null,null,null,{"$f":"SUM(F3:F6)","v":20},{"$f":"SUM(G3:G6)","v":1},null,null,"Var"]
[1,null,null,null,null,null,null,null,"Not equal to zero because you are not using all the data points","SD"]
[1,null,null,null,"E(x)","Σx*f(x)"]
[2,null,null,null,"SD of Discrete Random Variable","sqrt(Σ(x-mean)^2*f(x))"]
[2]
[2]
[2,null,null,null,null,"Weight mean"]
[2]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[3]
[4]
[4]
[4]
[4]
[null,null,"Must Equal Zero"]
[null,"Var"]
[null,"sd"]
[null,"Count"]

{"sheet":"EVSD(1)an","index":8,"n_rows":30,"n_cols":11,"rows_kept":30,"cut":false,"hidden":false,"merged":[[7,8,10,8]]}
["Mean and Standard Deviation from Raw Data",null,null,null,"Mean and Standard Deviation for Discrete Probability Distribution"]
[null,null,null,null,"x = # operating rooms in use for 1 day","Frequency (# of days)","Relative Frequency P(x) = f(x) = Probability","E(x) =X*f(x)","X - mu","(X-mu)^2",{"$f":"J2&\"*f(x)\"","v":"(X-mu)^2*f(x)"}]
["Mean",{"$f":"AVERAGE(A7:A26)","v":2.65},null,null,1,{"$f":"COUNTIF($A$7:$A$26,E3)","v":3},{"$f":"F3/$F$7","v":0.15},{"$f":"E3*G3","v":0.15},{"$f":"E3-$G$9","v":-1.6500000000000004},{"$f":"I3^2","v":2.722500000000001},{"$f":"J3*G3","v":0.40837500000000015}]
["STDEV.S",{"$f":"_xlfn.STDEV.S(A7:A26)","v":0.98808693416808457},null,null,2,{"$f":"COUNTIF($A$7:$A$26,E4)","v":5},{"$f":"F4/$F$7","v":0.25},{"$f":"E4*G4","v":0.5},{"$f":"E4-$G$9","v":-0.65000000000000036},{"$f":"I4^2","v":0.42250000000000049},{"$f":"J4*G4","v":0.10562500000000012}]
["STDEV.P",{"$f":"_xlfn.STDEV.P(A7:A26)","v":0.96306801421291111},null,null,3,{"$f":"COUNTIF($A$7:$A$26,E5)","v":8},{"$f":"F5/$F$7","v":0.4},{"$f":"E5*G5","v":1.2000000000000002},0.34999999999999964,0.12249999999999975,4.8999999999999905E-2]
["Raw Data = Xi","X - mu","(X-mu)^2",null,4,{"$f":"COUNTIF($A$7:$A$26,E6)","v":4},{"$f":"F6/$F$7","v":0.2},0.8,1.3499999999999996,1.8224999999999991,0.36449999999999982]
[1,{"$f":"A7-$B$3","v":-1.65},{"$f":"B7^2","v":2.7224999999999997},null,null,{"$f":"SUM(F3:F6)","v":20},{"$f":"SUM(G3:G6)","v":1},{"$f":"SUM(H3:H6)","v":2.6500000000000004},{"$f":"SUM(I3:I6)","v":-0.60000000000000142},"Var",{"$f":"SUM(K3:K6)","v":0.92749999999999999}]
[1,{"$f":"A8-$B$3","v":-1.65},{"$f":"B8^2","v":2.7224999999999997},null,null,null,null,null,"Not equal to zero because you are not using all the data points","SD",{"$f":"SQRT(K7)","v":0.96306801421291111}]
[1,-1.65,2.7224999999999997,null,"E(x)","Σx*f(x)",{"$f":"SUMPRODUCT(E3:E6,G3:G6)","v":2.6500000000000004}]
[2,-0.64999999999999991,0.42249999999999988,null,"SD of Discrete Random Variable","sqrt(Σ(x-mean)^2*f(x))",{"$f":"SQRT(SUMPRODUCT((E3:E6-G9)^2,G3:G6))","v":0.96306801421291111}]
[2,-0.64999999999999991,0.42249999999999988]
[2,-0.64999999999999991,0.42249999999999988]
[2,-0.64999999999999991,0.42249999999999988,null,null,"Weight mean",{"$f":"SUMPRODUCT(E3:E6,F3:F6)/F7","v":2.65}]
[2,-0.64999999999999991,0.42249999999999988]
[3,0.35000000000000009,0.12250000000000007]
[3,0.35000000000000009,0.12250000000000007]
[3,0.35000000000000009,0.12250000000000007]
[3,0.35000000000000009,0.12250000000000007]
[3,0.35000000000000009,0.12250000000000007]
[3,0.35000000000000009,0.12250000000000007]
[3,0.35000000000000009,0.12250000000000007]
[3,0.35000000000000009,0.12250000000000007]
[4,1.35,1.8225000000000002]
[4,1.35,1.8225000000000002]
[4,1.35,1.8225000000000002]
[4,1.35,1.8225000000000002]
[null,{"$f":"SUM(B7:B26)","v":-3.9968028886505635E-15},"Must Equal Zero"]
[null,"Var",{"$f":"SUM(C7:C26)/C30","v":0.92749999999999999}]
[null,"sd",{"$f":"SQRT(C28)","v":0.96306801421291111}]
[null,"Count",{"$f":"COUNT(A7:A26)","v":20}]

{"sheet":"EVSD(2)","index":9,"n_rows":125,"n_cols":6,"rows_kept":125,"cut":false,"hidden":false,"merged":[]}
["Unit Demand = x","Prob = f(x)",null,"(X - Mean)^2",null,"Mean"]
[500,0.1,null,{"$f":"(A2-$F$2)^2","v":84100},null,{"$f":"SUMPRODUCT(A2:A8,B2:B8)","v":790}]
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[800,0.2,null,100]
[900,0.2,null,12100]
[1000,0.15,null,44100]
[1100,0.05,null,96100]
[]
[]
["Mean = Expected Value",null," = monthly order quantity"]
["SD",null,null,{"$f":"SQRT(SUMPRODUCT(B2:B8,D2:D8))","v":170}]
[]
["Price per unit",125]
["Cost per unit",60]
["Assumed Units sold",500]
["Sales"]
["Expenses"]
["Gross Profit"]
[]
[]
[]
[null,"All Values"]
[null,500]
[null,500]
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[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1100]
[null,1100]
[null,1100]
[null,1100]
[null,1100]
["VAR.P",{"$f":"_xlfn.VAR.P(B24:B123)","v":28900}]
["STDEV.S",{"$f":"_xlfn.STDEV.P(B24:B123)","v":170}]

{"sheet":"EVSD(2)an","index":10,"n_rows":125,"n_cols":6,"rows_kept":125,"cut":false,"hidden":false,"merged":[]}
["Unit Demand = x","Prob = f(x)",null,"(X - Mean)^2",null,"Mean"]
[500,0.1,null,{"$f":"(A2-$F$2)^2","v":84100},null,{"$f":"SUMPRODUCT(A2:A8,B2:B8)","v":790}]
[600,0.15,null,36100]
[700,0.15,null,8100]
[800,0.2,null,100]
[900,0.2,null,12100]
[1000,0.15,null,44100]
[1100,0.05,null,96100]
[null,{"$f":"SUM(B2:B8)","v":1}]
[]
["Mean = Expected Value",{"$f":"SUMPRODUCT(A2:A8,B2:B8)","v":790}," = monthly order quantity"]
["SD",{"$f":"SQRT(SUMPRODUCT((A2:A8-B11)^2,B2:B8))","v":170},null,{"$f":"SQRT(SUMPRODUCT(B2:B8,D2:D8))","v":170}]
[]
["Price per unit",125]
["Cost per unit",60]
["Assumed Units sold",500]
["Sales",{"$f":"B16*B14","v":62500}]
["Expenses",{"$f":"B15*B11","v":47400}]
["Gross Profit",{"$f":"B17-B18","v":15100}]
[]
[]
[]
[null,"All Values"]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,500]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,600]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,700]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,800]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,900]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1000]
[null,1100]
[null,1100]
[null,1100]
[null,1100]
[null,1100]
["VAR.P",{"$f":"_xlfn.VAR.P(B24:B123)","v":28900}]
["STDEV.S",{"$f":"_xlfn.STDEV.P(B24:B123)","v":170}]

{"sheet":"EVSD(3)","index":11,"n_rows":8,"n_cols":5,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
["State of Economy","Prob. Of State of Economy","Stock A Return","Stock B Return","Stock C Return"]
["Boom",0.15,0.15,0.25,0.11]
["Normal",{"$f":"1-SUM(B2,B4)","v":0.29999999999999993},7.0000000000000007E-2,0.13,0.1]
["Bust",0.55000000000000004,-0.02,-0.13500000000000001,0.03]
[null,"E(Ri)"]
["Sd = Proxy for Risk","Standard Deviation"]
[null,"CV = SD/Mean"]
[null,"Mean/SD"]

{"sheet":"EVSD(3)an","index":12,"n_rows":8,"n_cols":5,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
["State of Economy","Prob. Of State of Economy","Stock A Return","Stock B Return","Stock C Return"]
["Boom",0.15,0.15,0.25,0.11]
["Normal",{"$f":"1-SUM(B2,B4)","v":0.29999999999999993},7.0000000000000007E-2,0.13,0.1]
["Bust",0.55000000000000004,-0.02,-0.13500000000000001,0.03]
[null,"E(Ri)",{"$f":"SUMPRODUCT($B$2:$B$4,C2:C4)","v":3.2499999999999994E-2},{"$f":"SUMPRODUCT($B$2:$B$4,D2:D4)","v":2.2499999999999742E-3},6.3E-2]
["Sd = Proxy for Risk","Standard Deviation",{"$f":"SQRT(SUMPRODUCT((C2:C4-C5)^2,$B$2:$B$4))","v":6.3314690238522056E-2},{"$f":"SQRT(SUMPRODUCT((D2:D4-D5)^2,$B$2:$B$4))","v":0.15640871938610074},3.661966684720111E-2]
[null,"CV = SD/Mean",{"$f":"C6/C5","v":1.9481443150314481},{"$f":"D6/D5","v":69.514986393823349},0.58126455313017633]
[null,"Mean/SD",{"$f":"C5/C6","v":0.5133089947619498},{"$f":"D5/D6","v":1.438538726505244E-2},1.7203870330899849]

{"sheet":"BDPD","index":13,"n_rows":30,"n_cols":17,"rows_kept":30,"cut":false,"hidden":false,"merged":[[12,15,13,15],[12,0,13,0],[12,5,13,5],[12,10,13,10],[12,11,13,11],[12,13,13,13],[12,14,13,14]]}
["pi =",0.2]
["1 - pi =",{"$f":"1-B1","v":0.8}]
["n =",4]
["Fixed # of Trials?","Yes"]
["Each Trial Independent?","Yes"]
["Success is?","Sale","S"]
["Fail is?","No Sale","NS"]
["Success or fail each trial?","Yes"]
["pi the same each Trial?","Yes"]
["Sample Space =",{"$f":"2^B3","v":16}]
[]
[{"$f":"\"Build Discrete Probability Distribution with \"&A3&\" \"&B3&\", \"&A1&\" \"&B1","v":"Build Discrete Probability Distribution with n = 4, pi = 0.2"}]
["Possible Outcomes","Attempted Sale",null,null,null,"# of Sales","Probability associated with each attempt",null,null,null,"Probability of Occurrence Calculation","Probability of Occurrence",null,"# of Sales (Random Variable X)","P(x)","P(x)"]
[null,"1st","2nd","3rd","4th",null,"1st","2nd","3rd","4th"]
[1,"S","S","S","S",{"$f":"COUNTIF(B15:E15,$C$6)","v":4},{"$f":"IF(B15=$C$6,$B$1,$B$2)","v":0.2},0.2,0.2,0.2,{"$f":"G15&\"*\"&H15&\"*\"&I15&\"*\"&J15&\" =\"","v":"0.2*0.2*0.2*0.2 ="},{"$f":"PRODUCT(G15:J15)","v":1.6000000000000005E-3},null,0,{"$f":"\"P(\"&N15&\") =\"","v":"P(0) ="},{"$f":"SUMIF($F$15:$F$30,N15,$L$15:$L$30)","v":0.40960000000000013}]
[2,"S","S","S","NS",3,0.2,0.2,0.2,0.8,"0.2*0.2*0.2*0.8 =",6.400000000000002E-3,null,1,{"$f":"\"P(\"&N16&\") =\"","v":"P(1) ="},{"$f":"SUMIF($F$15:$F$30,N16,$L$15:$L$30)","v":0.40960000000000013}]
[3,"S","S","NS","S",3,0.2,0.2,0.8,0.2,"0.2*0.2*0.8*0.2 =",6.400000000000002E-3,null,2,{"$f":"\"P(\"&N17&\") =\"","v":"P(2) ="},{"$f":"SUMIF($F$15:$F$30,N17,$L$15:$L$30)","v":0.15360000000000004}]
[4,"S","NS","S","S",3,0.2,0.8,0.2,0.2,"0.2*0.8*0.2*0.2 =",6.400000000000002E-3,null,3,{"$f":"\"P(\"&N18&\") =\"","v":"P(3) ="},{"$f":"SUMIF($F$15:$F$30,N18,$L$15:$L$30)","v":2.5600000000000008E-2}]
[5,"NS","S","S","S",3,0.8,0.2,0.2,0.2,"0.8*0.2*0.2*0.2 =",6.400000000000002E-3,null,4,{"$f":"\"P(\"&N19&\") =\"","v":"P(4) ="},{"$f":"SUMIF($F$15:$F$30,N19,$L$15:$L$30)","v":1.6000000000000005E-3}]
[6,"S","S","NS","NS",2,0.2,0.2,0.8,0.8,"0.2*0.2*0.8*0.8 =",2.5600000000000008E-2,null,null,null,{"$f":"SUM(P15:P19)","v":1.0000000000000002}]
[7,"S","NS","NS","S",2,0.2,0.8,0.8,0.2,"0.2*0.8*0.8*0.2 =",2.5600000000000008E-2]
[8,"NS","NS","S","S",2,0.8,0.8,0.2,0.2,"0.8*0.8*0.2*0.2 =",2.5600000000000008E-2,null,null,"E(x)",{"$f":"SUMPRODUCT(N15:N19,P15:P19)","v":0.80000000000000016},{"$f":"B3*B1","v":0.8}]
[9,"S","NS","S","NS",2,0.2,0.8,0.2,0.8,"0.2*0.8*0.2*0.8 =",2.5600000000000008E-2,null,null,"SD",{"$f":"SQRT(SUMPRODUCT((N15:N19-P22)^2,P15:P19))","v":0.8},{"$f":"SQRT(Q22*(1-B1))","v":0.8}]
[10,"NS","S","NS","S",2,0.8,0.2,0.8,0.2,"0.8*0.2*0.8*0.2 =",2.5600000000000008E-2]
[11,"NS","S","S","NS",2,0.8,0.2,0.2,0.8,"0.8*0.2*0.2*0.8 =",2.5600000000000008E-2]
[12,"S","NS","NS","NS",1,0.2,0.8,0.8,0.8,"0.2*0.8*0.8*0.8 =",0.10240000000000003]
[13,"NS","S","NS","NS",1,0.8,0.2,0.8,0.8,"0.8*0.2*0.8*0.8 =",0.10240000000000003]
[14,"NS","NS","S","NS",1,0.8,0.8,0.2,0.8,"0.8*0.8*0.2*0.8 =",0.10240000000000003]
[15,"NS","NS","NS","S",1,0.8,0.8,0.8,0.2,"0.8*0.8*0.8*0.2 =",0.10240000000000003]
[16,"NS","NS","NS","NS",0,0.8,0.8,0.8,0.8,"0.8*0.8*0.8*0.8 =",0.40960000000000013]

{"sheet":"B(1)","index":14,"n_rows":41,"n_cols":21,"rows_kept":41,"cut":false,"hidden":false,"merged":[[23,13,27,19],[23,20,27,20]]}
["An insurance agent has appointments with 4 clients tomorrow. From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?"]
["Binomial Experiment 4 Requirements:"]
[1,"Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a Fixed number of trials, n."]
[2,"Only 2 outcomes are possible on each indetical trial. Success or Failure."]
[3,"Probability of Success = p = (π \"pi\"). Probability of Failure = 1-p. Probability remains the same on each trial."]
[4,"The trials are independent (one does not affact the next)"]
[]
[1,"Fixed # of Identical Trials = n",null,"Yes"]
[2,"Each trial only results in S or F",null,"Yes"]
[3,"p remains the same for each trial",null,"Yes"]
[4,"All events are independent",null,"Yes"]
[]
[null,"An insurance agent has appointments with 4 clients tomorrow. From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?"]
[null,"Variables"]
[null,null,"Success",null,null,{"$f":"$D$18","v":0}]
[null,null,"Failure",null,null,{"$f":"$D$18","v":0}]
[null,null,"n",null,null,{"$f":"$D$18","v":0}]
[null,null,"x",null,null,{"$f":"$D$18","v":0}]
[null,null,"p (π)",null,null,{"$f":"$D$18","v":0}]
[]
[null,null,"X","P(x) = f(x)",null,null,{"$f":"B19&\" = \"&C19&\" = \"&D19&CHAR(10)&B8&\" = \"&D17","v":" = p (π) = \nFixed # of Identical Trials = n = "}]
[null,null,0,null,null,null,"P(x) = f(x)","P(x) = f(x)","SUM"]
[null,null,1,null,null,null,{"$f":"\"P(x = \"&F15&\")\"","v":"P(x = 0)"},null,null,null,"Success = s"]
[null,null,2,null,null,null,{"$f":"\"P(x <= \"&F19&\")\"","v":"P(x <= 0)"},null,null,null,"#S.P. = COMBIN",null,null,"An insurance agent has appointments with 4 clients tomorrow. From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?",null,null,null,null,null,null,"Define P(Event) = Sum of Probabilities of Sample Points in Event"]
[null,null,3,null,null,null,{"$f":"\"P(x > \"&F17&\")\"","v":"P(x > 0)"},null,null,null,"x = # policies Sold"]
[null,null,4,null,null,null,{"$f":"\"P(x >= \"&F16&\")\"","v":"P(x >= 0)"},null,null,null,"n = Trials or Steps"]
[null,null,null,null,null,null,{"$f":"\"P(x < \"&F18&\")\"","v":"P(x < 0)"},null,null,"s","p = Prob of success"]
[null,"Chart Title",null,null,null,null,null,null,null,"ns","(1-p) = Not a sale"]
[null,{"$f":"\"Binomial Distribution n = \"&D17&\", p = \"&D19","v":"Binomial Distribution n = , p = "},null,null,null,null,null,null,null,null,"# S.P.","C1","C2","C3","C4","P1","P2","P3","P4","P(S.P.)","Multiply"]
[null,null,null,null,null,null,null,null,null,null,1,"ns","s","s","s",{"$f":"VLOOKUP(L30,$J$27:$L$28,3,0)","v":0},0,0,0]
[null,null,null,null,null,null,null,null,null,null,2,"s","ns","s","s",0,0,0,0]
[null,null,null,null,null,null,null,null,null,null,3,"s","s","ns","s",0,0,0,0]
[null,null,null,null,null,null,null,null,null,null,4,"s","s","s","ns",0,0,0,0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Add"]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,"be sure to scroll up"]

{"sheet":"B(1)an","index":15,"n_rows":34,"n_cols":21,"rows_kept":34,"cut":false,"hidden":false,"merged":[[23,13,27,19],[23,20,27,20]]}
["An insurance agent has appointments with 4 clients tomorrow. From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?"]
["Binomial Experiment 4 Requirements:"]
[1,"Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a Fixed number of trials, n."]
[2,"Only 2 outcomes are possible on each indetical trial. Success or Failure."]
[3,"Probability of Success = p = (π \"pi\"). Probability of Failure = 1-p. Probability remains the same on each trial."]
[4,"The trials are independent (one does not affact the next)"]
[]
[1,"Fixed # of Identical Trials = n",null,"Yes",null,null,"Nominal Variable, Since 2 options use word \"bi\""]
[2,"Each trial only results in S or F",null,"Yes",null,null,"Sale"]
[3,"p remains the same for each trial",null,"Yes",null,null,"Not Sale"]
[4,"All events are independent",null,"Yes"]
[]
[null,"An insurance agent has appointments with 4 clients tomorrow. From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?"]
[null,"Variables"]
[null,"Make a sale","Success","s",null,{"$f":"$D$18","v":3}]
[null,"Not Make a sale","Failure","ns",null,{"$f":"$D$18","v":3}]
[null,"# of Fixed Trials = Steps = Attempts at Sale = Appointments","n",4,null,{"$f":"$D$18","v":3}]
[null,"Random Discrete Variable = # of sales in 4 tries","x",3,null,{"$f":"$D$18","v":3}]
[null,"Prob of Success (remains the same of trial)","p (π)",0.2,null,{"$f":"$D$18","v":3}]
[]
[null,null,"X","P(x) = f(x)",null,null,{"$f":"B19&\" = \"&C19&\" = \"&D19&CHAR(10)&B8&\" = \"&D17","v":"Prob of Success (remains the same of trial) = p (π) = 0.2\nFixed # of Identical Trials = n = 4"}]
[null,null,0,{"$f":"_xlfn.BINOM.DIST(C22,$D$17,$D$19,0)","v":0.40959999999999996},null,null,"P(x) = f(x)","P(x) = f(x)","SUM"]
[null,null,1,{"$f":"_xlfn.BINOM.DIST(C23,$D$17,$D$19,0)","v":0.40959999999999996},null,null,{"$f":"\"P(x = \"&F15&\")\"","v":"P(x = 3)"},{"$f":"_xlfn.BINOM.DIST(D18,D17,D19,0)","v":2.5600000000000005E-2},{"$f":"D25","v":2.5600000000000005E-2},null,"Success = s","Sale"]
[null,null,2,0.15359999999999996,null,null,{"$f":"\"P(x <= \"&F19&\")\"","v":"P(x <= 3)"},{"$f":"_xlfn.BINOM.DIST(D18,D17,D19,1)","v":0.99839999999999995},{"$f":"SUM(D22:D25)","v":0.99839999999999984},null,"#S.P. = COMBIN",{"$f":"COMBIN(L26,L25)","v":4},null,"An insurance agent has appointments with 4 clients tomorrow. From past data, the chance of making a sale is 1 in 5. What is likelihood that she will sell 3 policies in 4 tries?",null,null,null,null,null,null,"Define P(Event) = Sum of Probabilities of Sample Points in Event"]
[null,null,3,2.5600000000000005E-2,null,null,{"$f":"\"P(x > \"&F17&\")\"","v":"P(x > 3)"},{"$f":"1-_xlfn.BINOM.DIST(D18,D17,D19,1)","v":1.6000000000000458E-3},{"$f":"SUM(D26)","v":1.6000000000000005E-3},null,"x = # policies Sold",3]
[null,null,4,1.6000000000000005E-3,null,null,{"$f":"\"P(x >= \"&F16&\")\"","v":"P(x >= 3)"},{"$f":"1-_xlfn.BINOM.DIST(D18-1,D17,D19,1)","v":2.7200000000000002E-2},{"$f":"SUM(D25:D26)","v":2.7200000000000005E-2},null,"n = Trials or Steps",4]
[null,null,null,{"$f":"SUM(D22:D26)","v":0.99999999999999989},null,null,{"$f":"\"P(x < \"&F18&\")\"","v":"P(x < 3)"},{"$f":"_xlfn.BINOM.DIST(D18-1,D17,D19,1)","v":0.9728},{"$f":"SUM(D22:D24)","v":0.97279999999999989},"s","p = Prob of success",{"$f":"1/5","v":0.2}]
[null,"Chart Title",null,null,null,null,null,null,null,"ns","(1-p) = Not a sale",{"$f":"1-L27","v":0.8}]
[null,{"$f":"\"Binomial Distribution n = \"&D17&\", p = \"&D19","v":"Binomial Distribution n = 4, p = 0.2"},null,null,null,null,null,null,null,null,"# S.P.","C1","C2","C3","C4","P1","P2","P3","P4","P(S.P.)","Multiply"]
[null,null,null,null,null,null,null,null,null,null,1,"ns","s","s","s",{"$f":"VLOOKUP(L30,$J$27:$L$28,3,0)","v":0.8},0.2,0.2,0.2,{"$f":"PRODUCT(P30:S30)","v":6.400000000000002E-3}]
[null,null,null,null,null,null,null,null,null,null,2,"s","ns","s","s",0.2,0.8,0.2,0.2,{"$f":"PRODUCT(P31:S31)","v":6.400000000000002E-3}]
[null,null,null,null,null,null,null,null,null,null,3,"s","s","ns","s",0.2,0.2,0.8,0.2,6.400000000000002E-3]
[null,null,null,null,null,null,null,null,null,null,4,"s","s","s","ns",0.2,0.2,0.2,0.8,6.400000000000002E-3]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SUM(T30:T33)","v":2.5600000000000008E-2},"Add"]

{"sheet":"B(2)","index":16,"n_rows":64,"n_cols":7,"rows_kept":64,"cut":false,"hidden":false,"merged":[]}
["Binomial Experiment 4 Requirements:"]
[1,"Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a Fixed number of trials, n."]
[null,"Fixed # of Identical Trials = n","Yes"]
[2,"Only 2 outcomes are possible on each indetical trial. Success or Failure."]
[null,"Each trial only results in S or F","Yes"]
[3,"Probability of Success = p = (π \"pi\"). Probability of Failure = 1-p. Probability remains the same on each trial."]
[null,"p remains the same for each trial","Yes"]
[4,"The trials are independent (one does not affact the next)"]
[null,"All events are independent","Yes"]
[]
[null,"A flight from Oakland to Seattle occurs 6 times per day. The probability that any 1 flight is late is 10%. What is the probability that exactly 2 planes are late? Less than 2 are late? What is the mean and standard deviation?"]
[null,"Variables"]
[null,"Late Plane","Success","s"]
[null,"Plane On Time","Failure","f"]
[null,"# flights per day","n",6]
[null,"# plance late in 6 tries (1 day)","x",2]
[null,"Prob of success = prob plane late","p (π)",0.1]
[]
[null,{"$f":"B17&\" = \"&C17&\" = \"&D17&CHAR(10)&B3&\" = \"&D15","v":"Prob of success = prob plane late = p (π) = 0.1\nFixed # of Identical Trials = n = 6"}]
[null,"P(x) = f(x)","P(x) = f(x)",null,"Check"]
[2,{"$f":"\"P(x = \"&A21&\")\"","v":"P(x = 2)"}]
[2,{"$f":"\"P(x >= \"&A22&\")\"","v":"P(x >= 2)"}]
[2,{"$f":"\"P(x > \"&A23&\")\"","v":"P(x > 2)"}]
[2,{"$f":"\"P(x < \"&A24&\")\"","v":"P(x < 2)"}]
[2,{"$f":"\"P(x <= \"&A25&\")\"","v":"P(x <= 2)"}]
[]
["Mean","Σx*f(x)"]
["SD","sqrt(Σ(x-mean)^2*f(x))"]
["Mean","n*p"]
["SD","sqrt(n*p*(1-p))"]
[]
[null,null,"X","f(x)"]
[null,null,0,{"$f":"_xlfn.BINOM.DIST(C33,$F$34,$G$34,0)","v":0.53144100000000005},null,"n","pi"]
[null,null,1,{"$f":"_xlfn.BINOM.DIST(C34,$F$34,$G$34,0)","v":0.354294},null,6,0.1]
[null,null,2,9.8415000000000002E-2]
[null,null,3,1.4580000000000011E-2]
[null,null,4,1.2150000000000012E-3]
[null,null,5,5.3999999999999998E-5]
[null,null,6,1.0000000000000004E-6]
[null,null,null,{"$f":"SUM(D33:D39)","v":1}]
[]
[]
[null,"Traffic on Bridge Example, n = 7, pi = .15"]
[null,"Success = Stuck In Traffic","s"]
[null,"Failure = Not Stuck","f"]
[null,"n = Days across Bridge",7]
[null,"x = # times stuck in Traffic in 7 Tries"]
[null,"p (π) = Prob Stuck in Traffic",0.15]
[null,null,null,null,null,"Check"]
["x",3,null,null,null,{"$f":"SUM(D59)","v":6.1661988281250017E-2}]
["x","5 or more times",null,5,null,{"$f":"SUM(D61:D63)","v":1.2216445312500002E-3}]
["mean","Long Run Average = Expected Value",null,null,null,{"$f":"SUMPRODUCT(C56:C63,D56:D63)","v":1.0499999999999998}]
["Sd","Variation = Spread in data = Fair Mean?",null,null,null,{"$f":"SQRT(SUMPRODUCT((C56:C63-F52)^2,D56:D63))","v":0.94472218138455921}]
[]
[null,null,"x","p(x)","n","pi"]
[null,null,0,{"$f":"_xlfn.BINOM.DIST(C56,$E$56,$F$56,0)","v":0.32057708828125009},7,0.15]
[null,null,1,0.39600699140625001]
[null,null,2,0.20965076015625]
[null,null,3,6.1661988281250017E-2]
[null,null,4,1.0881527343750001E-2]
[null,null,5,1.1521617187500001E-3]
[null,null,6,6.7774218750000121E-5]
[null,null,7,1.70859375E-6]
[null,null,null,{"$f":"SUM(D56:D63)","v":1.0000000000000002}]

{"sheet":"B(2an)","index":17,"n_rows":64,"n_cols":7,"rows_kept":64,"cut":false,"hidden":false,"merged":[]}
["Binomial Experiment 4 Requirements:"]
[1,"Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a Fixed number of trials, n."]
[null,"Fixed # of Identical Trials = n","Yes"]
[2,"Only 2 outcomes are possible on each indetical trial. Success or Failure."]
[null,"Each trial only results in S or F","Yes"]
[3,"Probability of Success = p = (π \"pi\"). Probability of Failure = 1-p. Probability remains the same on each trial."]
[null,"p remains the same for each trial","Yes"]
[4,"The trials are independent (one does not affact the next)"]
[null,"All events are independent","Yes"]
[]
[null,"A flight from Oakland to Seattle occurs 6 times per day. The probability that any 1 flight is late is 10%. What is the probability that exactly 2 planes are late? Less than 2 are late? What is the mean and standard deviation?"]
[null,"Variables"]
[null,"Late Plane","Success","s"]
[null,"Plane On Time","Failure","f"]
[null,"# flights per day","n",6]
[null,"# plance late in 6 tries (1 day)","x",2]
[null,"Prob of success = prob plane late","p (π)",0.1]
[]
[null,{"$f":"B17&\" = \"&C17&\" = \"&D17&CHAR(10)&B3&\" = \"&D15","v":"Prob of success = prob plane late = p (π) = 0.1\nFixed # of Identical Trials = n = 6"}]
[null,"P(x) = f(x)","P(x) = f(x)",null,"Check"]
[2,{"$f":"\"P(x = \"&A21&\")\"","v":"P(x = 2)"},{"$f":"_xlfn.BINOM.DIST(A21,D15,D17,0)","v":9.8415000000000002E-2},null,{"$f":"D35","v":9.8415000000000002E-2}]
[2,{"$f":"\"P(x >= \"&A22&\")\"","v":"P(x >= 2)"},{"$f":"1-_xlfn.BINOM.DIST(A22-1,D15,D17,1)","v":0.11426500000000006},null,{"$f":"SUM(D35:D39)","v":0.11426500000000002}]
[2,{"$f":"\"P(x > \"&A23&\")\"","v":"P(x > 2)"},{"$f":"1-_xlfn.BINOM.DIST(A23,D15,D17,1)","v":1.5850000000000031E-2},null,{"$f":"SUM(D36:D39)","v":1.5850000000000013E-2}]
[2,{"$f":"\"P(x < \"&A24&\")\"","v":"P(x < 2)"},{"$f":"_xlfn.BINOM.DIST(A24-1,D15,D17,1)","v":0.88573499999999994},null,{"$f":"SUM(D33:D34)","v":0.88573500000000005}]
[2,{"$f":"\"P(x <= \"&A25&\")\"","v":"P(x <= 2)"},{"$f":"_xlfn.BINOM.DIST(A25,D15,D17,1)","v":0.98414999999999997},null,{"$f":"SUM(D33:D35)","v":0.98415000000000008}]
[]
["Mean","Σx*f(x)",{"$f":"SUMPRODUCT(C33:C39,D33:D39)","v":0.59999999999999987}]
["SD","sqrt(Σ(x-mean)^2*f(x))",{"$f":"SQRT(SUMPRODUCT((C33:C39-C27)^2,D33:D39))","v":0.73484692283495345}]
["Mean","n*p",{"$f":"D15*D17","v":0.60000000000000009}]
["SD","sqrt(n*p*(1-p))",{"$f":"SQRT(C29*(1-D17))","v":0.73484692283495356}]
[]
[null,null,"X","f(x)"]
[null,null,0,{"$f":"_xlfn.BINOM.DIST(C33,$F$34,$G$34,0)","v":0.53144100000000005},null,"n","pi"]
[null,null,1,{"$f":"_xlfn.BINOM.DIST(C34,$F$34,$G$34,0)","v":0.354294},null,6,0.1]
[null,null,2,9.8415000000000002E-2]
[null,null,3,1.4580000000000011E-2]
[null,null,4,1.2150000000000012E-3]
[null,null,5,5.3999999999999998E-5]
[null,null,6,1.0000000000000004E-6]
[null,null,null,{"$f":"SUM(D33:D39)","v":1}]
[]
[]
[null,"Traffic on Bridge Example, n = 7, pi = .15"]
[null,"Success = Stuck In Traffic","s"]
[null,"Failure = Not Stuck","f"]
[null,"n = Days across Bridge",7]
[null,"x = # times stuck in Traffic in 7 Tries"]
[null,"p (π) = Prob Stuck in Traffic",0.15]
[null,null,null,null,null,"Check"]
["x",3,{"$f":"_xlfn.BINOM.DIST(B50,C46,C48,0)","v":6.1661988281250017E-2},null,null,{"$f":"SUM(D59)","v":6.1661988281250017E-2}]
["x","5 or more times",{"$f":"1-_xlfn.BINOM.DIST(D51-1,C46,C48,1)","v":1.2216445312500657E-3},5,null,{"$f":"SUM(D61:D63)","v":1.2216445312500002E-3}]
["mean","Long Run Average = Expected Value",{"$f":"C46*C48","v":1.05},null,null,{"$f":"SUMPRODUCT(C56:C63,D56:D63)","v":1.0499999999999998}]
["Sd","Variation = Spread in data = Fair Mean?",{"$f":"SQRT(C52*(1-C48))","v":0.94472218138455921},null,null,{"$f":"SQRT(SUMPRODUCT((C56:C63-F52)^2,D56:D63))","v":0.94472218138455921}]
[]
[null,null,"x","p(x)","n","pi"]
[null,null,0,{"$f":"_xlfn.BINOM.DIST(C56,$E$56,$F$56,0)","v":0.32057708828125009},7,0.15]
[null,null,1,0.39600699140625001]
[null,null,2,0.20965076015625]
[null,null,3,6.1661988281250017E-2]
[null,null,4,1.0881527343750001E-2]
[null,null,5,1.1521617187500001E-3]
[null,null,6,6.7774218750000121E-5]
[null,null,7,1.70859375E-6]
[null,null,null,{"$f":"SUM(D56:D63)","v":1.0000000000000002}]

{"sheet":"B(2.5)","index":18,"n_rows":68,"n_cols":13,"rows_kept":68,"cut":false,"hidden":false,"merged":[]}
["Binomial Experiment 4 Requirements:"]
[1,"Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a Fixed number of trials, n."]
[null,"Fixed # of Identical Trials = n","Yes"]
[2,"Only 2 outcomes are possible on each identical trial. Success or Failure."]
[null,"Each trial only results in S or F","Yes"]
[3,"Probability of Success = p = (π \"pi\"). Probability of Failure = 1-p. Probability remains the same on each trial."]
[null,"p remains the same for each trial","Yes"]
[4,"The trials are independent (one does not affect the next)"]
[null,"All events are independent","Yes"]
[]
[null,{"$f":"\"Highline found that \"&TEXT(D17,\"0.00%\")&\" of its students withdraw from Accounting 202. In the current class that has \"&D15&\" students enrolled, what is the probability that \"&K16&\" will withdraw; \"&K18&\" will withdraw; \"&K17&\" will withdraw; and what is the expected number (average) of withdrawals?\"","v":"Highline found that 16.00% of its students withdraw from Accounting 202. In the current class that has 42 students enrolled, what is the probability that 2 or fewer will withdraw; more than 3 will withdraw; exactly 4 will withdraw; and what is the expected number (average) of withdrawals?"}]
[null,"Variables"]
[null,"Withdraw Accounting 202","Success"]
[null,{"$f":"\"Not \"&B13","v":"Not Withdraw Accounting 202"},"Failure"]
[null,null,"n",42,null,"n","x","P(x) = f(x)","P(x) = f(x)",null,null,null,"Check"]
[null,{"$f":"\"# successes = # that \"&B13","v":"# successes = # that Withdraw Accounting 202"},"x",null,null,{"$f":"$D$15","v":42},2,{"$f":"\"P(\"&K16&\")\"","v":"P(2 or fewer)"},"P(x) = f(x)",{"$f":"\"P(x <= \"&G16&\")\"","v":"P(x <= 2)"},{"$f":"G16&\" or fewer\"","v":"2 or fewer"},null,{"$f":"SUM(J25:J27)","v":2.6568524044642175E-2}]
[null,{"$f":"\"Probability of \"&B13","v":"Probability of Withdraw Accounting 202"},"p (π)",0.16,null,{"$f":"$D$15","v":42},4,{"$f":"\"P(\"&K17&\")\"","v":"P(exactly 4)"},null,{"$f":"\"P(x = \"&G17&\")\"","v":"P(x = 4)"},{"$f":"\"exactly \"&G17","v":"exactly 4"},null,{"$f":"J29","v":9.7283526381498023E-2}]
[null,null,null,null,null,{"$f":"$D$15","v":42},3,{"$f":"\"P(\"&K18&\")\"","v":"P(more than 3)"},null,{"$f":"\"P(x > \"&G18&\")\"","v":"P(x > 3)"},{"$f":"\"more than \"&G18","v":"more than 3"},null,{"$f":"SUM(J29:J67)","v":0.92104803867301299}]
[null,null,null,null,null,null,null,"Mean = E(x) = n*p",null,null,null,null,{"$f":"SUMPRODUCT(I25:I67,J25:J67)","v":6.7200000000000006}]
[]
[]
[null,{"$f":"\"Binomial Distribution, n = \"&D15&\" p = \"&D17","v":"Binomial Distribution, n = 42 p = 0.16"}]
[]
[null,null,null,null,null,null,null,null,"x","P(x)","n","p"]
[null,null,null,null,null,null,null,null,0,{"$f":"_xlfn.BINOM.DIST(I25,$K$25,$L$25,0)","v":6.6028284607986447E-4},{"$f":"D15","v":42},{"$f":"D17","v":0.16}]
[null,null,null,null,null,null,null,null,1,{"$f":"_xlfn.BINOM.DIST(I26,$K$25,$L$25,0)","v":5.2822627686389175E-3}]
[null,null,null,null,null,null,null,null,2,2.0625978429923395E-2]
[null,null,null,null,null,null,null,null,3,5.2383437282345076E-2]
[null,null,null,null,null,null,null,null,4,9.7283526381498023E-2]
[null,null,null,null,null,null,null,null,5,0.14082948580940668]
[null,null,null,null,null,null,null,null,6,0.1654187611094618]
[null,null,null,null,null,null,null,null,7,0.1620428680255952]
[null,null,null,null,null,null,null,null,8,0.13503572335466266]
[null,null,null,null,null,null,null,null,9,9.716856283721749E-2]
[null,null,null,null,null,null,null,null,10,6.1077382354822476E-2]
[null,null,null,null,null,null,null,null,11,3.3843744335139744E-2]
[null,null,null,null,null,null,null,null,12,1.665327102205286E-2]
[null,null,null,null,null,null,null,null,13,7.3201191305726949E-3]
[null,null,null,null,null,null,null,null,14,2.8882102692055454E-3]
[null,null,null,null,null,null,null,null,15,1.0269192068286435E-3]
[null,null,null,null,null,null,null,null,16,3.3008117362349224E-4]
[null,null,null,null,null,null,null,null,17,9.6158100999560925E-5]
[null,null,null,null,null,null,null,null,18,2.543865105808478E-5]
[null,null,null,null,null,null,null,null,19,6.1205776981858412E-6]
[null,null,null,null,null,null,null,null,20,1.3406979719835603E-6]
[null,null,null,null,null,null,null,null,21,2.6753156810556289E-7]
[null,null,null,null,null,null,null,null,22,4.8642103291920624E-8]
[null,null,null,null,null,null,null,null,23,8.0566630711254896E-9]
[null,null,null,null,null,null,null,null,24,1.2148936377094062E-9]
[null,null,null,null,null,null,null,null,25,1.6661398460014769E-10]
[null,null,null,null,null,null,null,null,26,2.0750459620531107E-11]
[null,null,null,null,null,null,null,null,27,2.3422035550511476E-12]
[null,null,null,null,null,null,null,null,28,2.3900036276032117E-13]
[null,null,null,null,null,null,null,null,29,2.1977044851523762E-14]
[null,null,null,null,null,null,null,null,30,1.8139783052051222E-15]
[null,null,null,null,null,null,null,null,31,1.3374955245752239E-16]
[null,null,null,null,null,null,null,null,32,8.7574111728138882E-18]
[null,null,null,null,null,null,null,null,33,5.0547827837309755E-19]
[null,null,null,null,null,null,null,null,34,2.548629974990406E-20]
[null,null,null,null,null,null,null,null,35,1.1096076081590919E-21]
[null,null,null,null,null,null,null,null,36,4.1096578079966202E-23]
[null,null,null,null,null,null,null,null,37,1.2693923731263665E-24]
[null,null,null,null,null,null,null,null,38,3.1814345191137052E-26]
[null,null,null,null,null,null,null,null,39,6.2152566917972102E-28]
[null,null,null,null,null,null,null,null,40,8.8789381311389137E-30]
[null,null,null,null,null,null,null,null,41,8.2498844424054077E-32]
[null,null,null,null,null,null,null,null,42,3.7414441915670851E-34]
[null,null,null,null,null,null,null,null,null,{"$f":"SUM(J25:J67)","v":1.0000000000000004}]

{"sheet":"B(2.5an)","index":19,"n_rows":68,"n_cols":13,"rows_kept":68,"cut":false,"hidden":false,"merged":[]}
["Binomial Experiment 4 Requirements:"]
[1,"Experiment consists of a sequence of n identical trials. Random Variable counts the number of successes in a Fixed number of trials, n."]
[null,"Fixed # of Identical Trials = n","Yes"]
[2,"Only 2 outcomes are possible on each identical trial. Success or Failure."]
[null,"Each trial only results in S or F","Yes"]
[3,"Probability of Success = p = (π \"pi\"). Probability of Failure = 1-p. Probability remains the same on each trial."]
[null,"p remains the same for each trial","Yes"]
[4,"The trials are independent (one does not affect the next)"]
[null,"All events are independent","Yes"]
[]
[null,{"$f":"\"Highline found that \"&TEXT(D17,\"0.00%\")&\" of its students withdraw from Accounting 202. In the current class that has \"&D15&\" students enrolled, what is the probability that \"&K16&\" will withdraw; \"&K18&\" will withdraw; \"&K17&\" will withdraw; and what is the expected number (average) of withdrawals?\"","v":"Highline found that 16.00% of its students withdraw from Accounting 202. In the current class that has 42 students enrolled, what is the probability that 2 or fewer will withdraw; more than 3 will withdraw; exactly 4 will withdraw; and what is the expected number (average) of withdrawals?"}]
[null,"Variables"]
[null,"Withdraw Accounting 202","Success"]
[null,{"$f":"\"Not \"&B13","v":"Not Withdraw Accounting 202"},"Failure"]
[null,null,"n",42,null,"n","x","P(x) = f(x)","P(x) = f(x)",null,null,null,"Check"]
[null,{"$f":"\"# successes = # that \"&B13","v":"# successes = # that Withdraw Accounting 202"},"x",null,null,{"$f":"$D$15","v":42},2,{"$f":"\"P(\"&K16&\")\"","v":"P(2 or fewer)"},{"$f":"_xlfn.BINOM.DIST(G16,F16,D17,1)","v":2.656852404464214E-2},{"$f":"\"P(x <= \"&G16&\")\"","v":"P(x <= 2)"},{"$f":"G16&\" or fewer\"","v":"2 or fewer"},null,{"$f":"SUM(J25:J27)","v":2.6568524044642175E-2}]
[null,{"$f":"\"Probability of \"&B13","v":"Probability of Withdraw Accounting 202"},"p (π)",0.16,null,{"$f":"$D$15","v":42},4,{"$f":"\"P(\"&K17&\")\"","v":"P(exactly 4)"},{"$f":"_xlfn.BINOM.DIST(G17,F17,D17,0)","v":9.7283526381498023E-2},{"$f":"\"P(x = \"&G17&\")\"","v":"P(x = 4)"},{"$f":"\"exactly \"&G17","v":"exactly 4"},null,{"$f":"J29","v":9.7283526381498023E-2}]
[null,null,null,null,null,{"$f":"$D$15","v":42},3,{"$f":"\"P(\"&K18&\")\"","v":"P(more than 3)"},{"$f":"1-_xlfn.BINOM.DIST(G18,F18,D17,1)","v":0.92104803867301277},{"$f":"\"P(x > \"&G18&\")\"","v":"P(x > 3)"},{"$f":"\"more than \"&G18","v":"more than 3"},null,{"$f":"SUM(J29:J67)","v":0.92104803867301299}]
[null,null,null,null,null,null,null,"Mean = E(x) = n*p",{"$f":"D15*D17","v":6.72},null,null,null,{"$f":"SUMPRODUCT(I25:I67,J25:J67)","v":6.7200000000000006}]
[]
[]
[null,{"$f":"\"Binomial Distribution, n = \"&D15&\" p = \"&D17","v":"Binomial Distribution, n = 42 p = 0.16"}]
[]
[null,null,null,null,null,null,null,null,"x","P(x)","n","p"]
[null,null,null,null,null,null,null,null,0,{"$f":"_xlfn.BINOM.DIST(I25,$K$25,$L$25,0)","v":6.6028284607986447E-4},{"$f":"D15","v":42},{"$f":"D17","v":0.16}]
[null,null,null,null,null,null,null,null,1,{"$f":"_xlfn.BINOM.DIST(I26,$K$25,$L$25,0)","v":5.2822627686389175E-3}]
[null,null,null,null,null,null,null,null,2,2.0625978429923395E-2]
[null,null,null,null,null,null,null,null,3,5.2383437282345076E-2]
[null,null,null,null,null,null,null,null,4,9.7283526381498023E-2]
[null,null,null,null,null,null,null,null,5,0.14082948580940668]
[null,null,null,null,null,null,null,null,6,0.1654187611094618]
[null,null,null,null,null,null,null,null,7,0.1620428680255952]
[null,null,null,null,null,null,null,null,8,0.13503572335466266]
[null,null,null,null,null,null,null,null,9,9.716856283721749E-2]
[null,null,null,null,null,null,null,null,10,6.1077382354822476E-2]
[null,null,null,null,null,null,null,null,11,3.3843744335139744E-2]
[null,null,null,null,null,null,null,null,12,1.665327102205286E-2]
[null,null,null,null,null,null,null,null,13,7.3201191305726949E-3]
[null,null,null,null,null,null,null,null,14,2.8882102692055454E-3]
[null,null,null,null,null,null,null,null,15,1.0269192068286435E-3]
[null,null,null,null,null,null,null,null,16,3.3008117362349224E-4]
[null,null,null,null,null,null,null,null,17,9.6158100999560925E-5]
[null,null,null,null,null,null,null,null,18,2.543865105808478E-5]
[null,null,null,null,null,null,null,null,19,6.1205776981858412E-6]
[null,null,null,null,null,null,null,null,20,1.3406979719835603E-6]
[null,null,null,null,null,null,null,null,21,2.6753156810556289E-7]
[null,null,null,null,null,null,null,null,22,4.8642103291920624E-8]
[null,null,null,null,null,null,null,null,23,8.0566630711254896E-9]
[null,null,null,null,null,null,null,null,24,1.2148936377094062E-9]
[null,null,null,null,null,null,null,null,25,1.6661398460014769E-10]
[null,null,null,null,null,null,null,null,26,2.0750459620531107E-11]
[null,null,null,null,null,null,null,null,27,2.3422035550511476E-12]
[null,null,null,null,null,null,null,null,28,2.3900036276032117E-13]
[null,null,null,null,null,null,null,null,29,2.1977044851523762E-14]
[null,null,null,null,null,null,null,null,30,1.8139783052051222E-15]
[null,null,null,null,null,null,null,null,31,1.3374955245752239E-16]
[null,null,null,null,null,null,null,null,32,8.7574111728138882E-18]
[null,null,null,null,null,null,null,null,33,5.0547827837309755E-19]
[null,null,null,null,null,null,null,null,34,2.548629974990406E-20]
[null,null,null,null,null,null,null,null,35,1.1096076081590919E-21]
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["p",0.16]
[]
[]
["X","p(x)"]
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[{"$f":"IF(ROWS(A$6:A9)<=$B$1+1,ROWS(A$6:A9)-1,\"\")","v":3},{"$f":"IF(ROWS(A$6:A9)<=$B$1+1,_xlfn.BINOM.DIST(A9,$B$1,$B$2,0),\"\")","v":9.592778249994241E-2}]
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[{"$f":"IF(ROWS(A$6:A11)<=$B$1+1,ROWS(A$6:A11)-1,\"\")","v":5},{"$f":"IF(ROWS(A$6:A11)<=$B$1+1,_xlfn.BINOM.DIST(A11,$B$1,$B$2,0),\"\")","v":3.4803730612224006E-3},null,"As n increases, distributions approached Bell"]
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[{"$f":"IF(ROWS(A$6:A21)<=$B$1+1,ROWS(A$6:A21)-1,\"\")","v":""},{"$f":"IF(ROWS(A$6:A21)<=$B$1+1,_xlfn.BINOM.DIST(A21,$B$1,$B$2,0),\"\")","v":""}]
[{"$f":"IF(ROWS(A$6:A22)<=$B$1+1,ROWS(A$6:A22)-1,\"\")","v":""},{"$f":"IF(ROWS(A$6:A22)<=$B$1+1,_xlfn.BINOM.DIST(A22,$B$1,$B$2,0),\"\")","v":""}]
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[{"$f":"IF(ROWS(A$6:A32)<=$B$1+1,ROWS(A$6:A32)-1,\"\")","v":""},{"$f":"IF(ROWS(A$6:A32)<=$B$1+1,_xlfn.BINOM.DIST(A32,$B$1,$B$2,0),\"\")","v":""}]
[{"$f":"IF(ROWS(A$6:A33)<=$B$1+1,ROWS(A$6:A33)-1,\"\")","v":""},{"$f":"IF(ROWS(A$6:A33)<=$B$1+1,_xlfn.BINOM.DIST(A33,$B$1,$B$2,0),\"\")","v":""}]
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[{"$f":"IF(ROWS(A$6:A40)<=$B$1+1,ROWS(A$6:A40)-1,\"\")","v":""},{"$f":"IF(ROWS(A$6:A40)<=$B$1+1,_xlfn.BINOM.DIST(A40,$B$1,$B$2,0),\"\")","v":""}]
[{"$f":"IF(ROWS(A$6:A41)<=$B$1+1,ROWS(A$6:A41)-1,\"\")","v":""},{"$f":"IF(ROWS(A$6:A41)<=$B$1+1,_xlfn.BINOM.DIST(A41,$B$1,$B$2,0),\"\")","v":""}]
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[{"$f":"IF(ROWS(A$6:A45)<=$B$1+1,ROWS(A$6:A45)-1,\"\")","v":""},{"$f":"IF(ROWS(A$6:A45)<=$B$1+1,_xlfn.BINOM.DIST(A45,$B$1,$B$2,0),\"\")","v":""}]
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[{"$f":"IF(ROWS(A$9:A85)<=$B$1+1,ROWS(A$9:A85)-1,\"\")","v":""},{"$f":"IF(ROWS(A$9:A85)<=$B$1+1,_xlfn.BINOM.DIST(A85,$B$1,$B$2,0),\"\")","v":""},""]
[{"$f":"IF(ROWS(A$9:A86)<=$B$1+1,ROWS(A$9:A86)-1,\"\")","v":""},{"$f":"IF(ROWS(A$9:A86)<=$B$1+1,_xlfn.BINOM.DIST(A86,$B$1,$B$2,0),\"\")","v":""},""]
[{"$f":"IF(ROWS(A$9:A87)<=$B$1+1,ROWS(A$9:A87)-1,\"\")","v":""},{"$f":"IF(ROWS(A$9:A87)<=$B$1+1,_xlfn.BINOM.DIST(A87,$B$1,$B$2,0),\"\")","v":""},""]
[{"$f":"IF(ROWS(A$9:A88)<=$B$1+1,ROWS(A$9:A88)-1,\"\")","v":""},{"$f":"IF(ROWS(A$9:A88)<=$B$1+1,_xlfn.BINOM.DIST(A88,$B$1,$B$2,0),\"\")","v":""},""]

{"sheet":"B(5)","index":22,"n_rows":21,"n_cols":2,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["n",10]
["p",0.4]
["X",6]
["Comparative Operator","<="]
["Result",{"$f":"B4&B3","v":"<=6"}]
["P(x<=3)"]
[]
["X","P(x)"]
[0]
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[]
[null,{"$f":"SUM(B9:B19)","v":0}]

{"sheet":"B(5an)","index":23,"n_rows":21,"n_cols":4,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
["n",10,null,{"$f":"\"Binomial Distribution at n = \"&B1&\", p = \"&B2","v":"Binomial Distribution at n = 10, p = 0.4"}]
["p",0.4]
["X",3]
["Comparative Operator","<="]
["Result",{"$f":"B4&B3","v":"<=3"}]
[{"$f":"C8","v":"P(x<=3) = 0.3823"},{"$f":"ROUND(_xlfn.BINOM.DIST(B3,B1,B2,1),4)","v":0.38229999999999997}]
[]
["X","P(x)",{"$f":"\"P(x\"&B5&\") = \"&B6","v":"P(x<=3) = 0.3823"}]
[0,{"$f":"_xlfn.BINOM.DIST(A9,$B$1,$B$2,0)","v":6.0466176E-3},{"$f":"IF(A9<=$B$3,B9,\"\")","v":6.0466176E-3}]
[1,{"$f":"_xlfn.BINOM.DIST(A10,$B$1,$B$2,0)","v":4.0310783999999981E-2},{"$f":"IF(A10<=$B$3,B10,\"\")","v":4.0310783999999981E-2}]
[2,0.12093235200000005,0.12093235200000005]
[3,0.21499084800000007,0.21499084800000007]
[4,0.25082265600000009,""]
[5,0.20065812480000006,""]
[6,0.11147673600000005,""]
[7,4.2467328000000006E-2,""]
[8,1.0616832000000007E-2,""]
[9,1.5728639999999985E-3,""]
[10,1.0485760000000014E-4,""]
[]
[null,{"$f":"SUM(B9:B19)","v":1.0000000000000002}]

{"sheet":"P(1)","index":24,"n_rows":69,"n_cols":7,"rows_kept":69,"cut":false,"hidden":false,"merged":[]}
[null,"Poisson Probability Distribution can be used to estimate the number of occurrences over a specified interval of time or space"]
[null,"Properties of a Poisson Experiment:"]
[null,"The probability of an occurrence is the same for any two intervals of equal length"]
[null,"The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval"]
[null,"No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gest quite small."]
[null,"Mean = Var"]
[null,"Excel function: POISSON.DIST\nPOISSON.DIST(x,mean,cumulative (0 = exact, 1 = cumulative))"]
[]
[]
[null,"x = Number of Web visitors",7,"per","minutes"]
[null,"Business =","Your Cool Web Site"]
[null,{"$f":"B10&\" arrive at a rate of \"&C10&\" per minute at \"&C11","v":"x = Number of Web visitors arrive at a rate of 7 per minute at Your Cool Web Site"}]
[null,"Assumption 1","Probability is the same for any 1 minute interval"]
[null,"Assumption 2","Arrival or nonarrival of a web visitor in a 1 minute period is independent of the arrival or nonarrival in any other 1 minute period"]
[null,"Mean",{"$f":"$C$10","v":7},"visits","per",1,"minute"]
["a","x",0,"visits","per",1,"minute"]
[null,"Mean"]
[null,{"$f":"\"P(\"&C16&\" \"&D16&\" \"&E16&\" \"&F16&\" \"&G16&\")\"","v":"P(0 visits per 1 minute)"}]
[null,"P(x) = (mu^x*e^-mu)/X!)"]
["b","x",2]
[null,"P(2 or more in 1 minute)"]
["c","x",1,{"$f":"1/2","v":0.5},"minutes"]
[null,"Mean"]
[null,"P(1 or more in 30 sec.)"]
["d","x",5]
[null,"P(5 or more in 1 minute)"]
[null,"x",4]
[null,"P(4 or less in 1 minute)"]
[]
[]
[]
[]
[]
[]
[null,null,{"$f":"SUM(C39:C40)","v":7.2950557244361291E-3}]
[]
[]
[null,"x","p(x)"]
[null,0,{"$f":"_xlfn.POISSON.DIST(B39,$C$15,0)","v":9.1188196555451624E-4}]
[null,1,{"$f":"_xlfn.POISSON.DIST(B40,$C$15,0)","v":6.3831737588816127E-3}]
[null,2,2.2341108156085653E-2]
[null,3,5.2129252364199866E-2]
[null,4,9.1226191637349782E-2]
[null,5,0.12771666829228964]
[null,6,0.14900277967433789]
[null,7,0.14900277967433789]
[null,8,0.13037743221504566]
[null,9,0.10140466950059109]
[null,10,7.0983268650413753E-2]
[null,11,4.5171170959354211E-2]
[null,12,2.6349849726289985E-2]
[null,13,1.4188380621848417E-2]
[null,14,7.0941903109242224E-3]
[null,15,3.3106221450979714E-3]
[null,16,1.4483971884803614E-3]
[null,17,5.9639884231544313E-4]
[null,18,2.3193288312267158E-4]
[null,19,8.5448956939931849E-5]
[null,20,2.9907134928976161E-5]
[null,21,9.969044976325377E-6]
[null,22,3.1719688561035243E-6]
[null,23,9.653818257706377E-7]
[null,24,2.8156969918310329E-7]
[null,25,7.883951577126872E-8]
[null,26,2.122602347688008E-8]
[null,27,5.5030431236355447E-9]
[null,28,1.3757607809088994E-9]
[null,29,3.3208018849525003E-10]
[null,30,7.7485377315558659E-11]

{"sheet":"P(1an)","index":25,"n_rows":69,"n_cols":7,"rows_kept":69,"cut":false,"hidden":false,"merged":[]}
[null,"Poisson Probability Distribution can be used to estimate the number of occurrences over a specified interval of time or space"]
[null,"Properties of a Poisson Experiment:"]
[null,"The probability of an occurrence is the same for any two intervals of equal length"]
[null,"The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval"]
[null,"No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gest quite small."]
[null,"Mean = Var"]
[null,"Excel function: POISSON.DIST\nPOISSON.DIST(x,mean,cumulative (0 = exact, 1 = cumulative))"]
[]
[]
[null,"x = Number of Web visitors",7,"per","minutes"]
[null,"Business =","Your Cool Web Site"]
[null,{"$f":"B10&\" arrive at a rate of \"&C10&\" per minute at \"&C11","v":"x = Number of Web visitors arrive at a rate of 7 per minute at Your Cool Web Site"}]
[null,"Assumption 1","Probability is the same for any 1 minute interval"]
[null,"Assumption 2","Arrival or nonarrival of a web visitor in a 1 minute period is independent of the arrival or nonarrival in any other 1 minute period"]
[null,"Mean",{"$f":"$C$10","v":7},"visits","per",1,"minute"]
["a","x",0,"visits","per",1,"minute"]
[null,"Mean",{"$f":"C15","v":7}]
[null,{"$f":"\"P(\"&C16&\" \"&D16&\" \"&E16&\" \"&F16&\" \"&G16&\")\"","v":"P(0 visits per 1 minute)"},{"$f":"_xlfn.POISSON.DIST(C16,C17,0)","v":9.1188196555451624E-4}]
[null,"P(x) = (mu^x*e^-mu)/X!)",{"$f":"(C17^C16*EXP(1)^-C17)/FACT(C16)","v":9.1188196555451646E-4}]
["b","x",2]
[null,"P(2 or more in 1 minute)",{"$f":"1-_xlfn.POISSON.DIST(C20-1,C17,1)","v":0.99270494427556388}]
["c","x",1,{"$f":"1/2","v":0.5},"minutes"]
[null,"Mean",{"$f":"C15*D22","v":3.5}]
[null,"P(1 or more in 30 sec.)",{"$f":"1-_xlfn.POISSON.DIST(C22-1,C23,1)","v":0.96980261657768152}]
["d","x",5]
[null,"P(5 or more in 1 minute)",{"$f":"1-_xlfn.POISSON.DIST(C25-1,C17,1)","v":0.82700839211792865}]
[null,"x",4]
[null,"P(4 or less in 1 minute)",{"$f":"_xlfn.POISSON.DIST(C27,C17,1)","v":0.17299160788207132}]
[]
[]
[]
[]
[]
[]
[null,null,{"$f":"SUM(C39:C40)","v":7.2950557244361291E-3}]
[]
[]
[null,"x","p(x)"]
[null,0,{"$f":"_xlfn.POISSON.DIST(B39,$C$15,0)","v":9.1188196555451624E-4}]
[null,1,{"$f":"_xlfn.POISSON.DIST(B40,$C$15,0)","v":6.3831737588816127E-3}]
[null,2,2.2341108156085653E-2]
[null,3,5.2129252364199866E-2]
[null,4,9.1226191637349782E-2]
[null,5,0.12771666829228964]
[null,6,0.14900277967433789]
[null,7,0.14900277967433789]
[null,8,0.13037743221504566]
[null,9,0.10140466950059109]
[null,10,7.0983268650413753E-2]
[null,11,4.5171170959354211E-2]
[null,12,2.6349849726289985E-2]
[null,13,1.4188380621848417E-2]
[null,14,7.0941903109242224E-3]
[null,15,3.3106221450979714E-3]
[null,16,1.4483971884803614E-3]
[null,17,5.9639884231544313E-4]
[null,18,2.3193288312267158E-4]
[null,19,8.5448956939931849E-5]
[null,20,2.9907134928976161E-5]
[null,21,9.969044976325377E-6]
[null,22,3.1719688561035243E-6]
[null,23,9.653818257706377E-7]
[null,24,2.8156969918310329E-7]
[null,25,7.883951577126872E-8]
[null,26,2.122602347688008E-8]
[null,27,5.5030431236355447E-9]
[null,28,1.3757607809088994E-9]
[null,29,3.3208018849525003E-10]
[null,30,7.7485377315558659E-11]

{"sheet":"H","index":26,"n_rows":24,"n_cols":9,"rows_kept":24,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,"New Excel 2010 Function:"]
[null,null,null,null,null,null,null,null,"HYPGEOM.DIST"]
[null,null,null,null,null,null,null,null,"Swee vieo:"]
[null,null,null,null,null,null,null,null,"Excel 2010 Statistics #39: HYPGEOM.DIST and Conditional Probabilities New Excel 2010 Function"]