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{"sheet":"(1)","index":0,"n_rows":19,"n_cols":12,"rows_kept":19,"cut":false,"hidden":false,"merged":[]}
[null,"known to be uniformly distributed"]
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[null,{"$f":"\"f(x) = 1/(\"&C3&\" - \"&C2&\") = \"&1/(C3-C2)&\" = height = h\"","v":"f(x) = 1/(1.5 - 1) = 2 = height = h"},{"$f":"1/(C3-C2)","v":2}]
[null,"Area = 1/(b-a)*(x2-x1)"]
[null,"width = b - a =",{"$f":"C3-C2","v":0.5}]
[null,"f(x)"]
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["d","x1",1.2]
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[null,"known to be uniformly distributed"]
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[]
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[null,"P(x<15) = P(10<x<15) = P(10<=x<=15) = w*h =",{"$f":"C15*C14","v":0.5},null,null,{"$f":"\"** Note: because lines have no area: P(\"&C12&\"<=x<=\"&C13&\")\"&\" = P(\"&C12&\"<x<\"&C13&\")\"","v":"** Note: because lines have no area: P(10<=x<=15) = P(10<x<15)"}]
[]
["c","x1",12]
[null,"x2",18]
[null,"height =",{"$f":"$C$4","v":0.1}]
[null,"width =",{"$f":"C19-C18","v":6}]
[null,"P(12<x<18) = w*h",{"$f":"C21*C20","v":0.60000000000000009},null,null,{"$f":"\"** Note: because lines have no area: P(\"&C18&\"<=x<=\"&C19&\")\"&\" = P(\"&C18&\"<x<\"&C19&\")\"","v":"** Note: because lines have no area: P(12<=x<=18) = P(12<x<18)"}]
[]
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[null,"Var",{"$f":"C25^2","v":8.3333333333333357}]

{"sheet":"(3)","index":2,"n_rows":21,"n_cols":9,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
[null,"quoted time =",125,"min"]
[null,"a",120,"min"]
[null,"b",140,"min"]
[null,"height = f(x) = 1/(b-a)",{"$f":"1/(C3-C2)","v":0.05}]
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[]
[]
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[null,{"$f":"B4&\" = \"&C4","v":"height = f(x) = 1/(b-a) = 0.05"}]
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[null,"x2",130]
[null,"P(X<=125)",{"$f":"$C$4*(C14-C13)","v":0.5}]
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[null,"x2",140]
[null,"P(X>130)",{"$f":"$C$4*(C18-C17)","v":0.25}]
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[null,"a",0]
[null,"b",1]
[null,"f(x) = 1/(1-0) = 1 = height =",{"$f":"1/(C2-C1)","v":1}]
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["a",null,2]
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[null,"f(x) =1",1]
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[]
[]
["b","x1",0.25]
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[]
["c","x1",0]
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["e","E(x) = (a+b)/2",{"$f":"(C2-C1)/2","v":0.5}]
[null,"E(rand)",{"$f":"AVERAGE(C31:C80)","v":0.53803745041526729}]
[null,"SD = SQRT((b-a)^2/12)",{"$f":"SQRT((C2-C1)^2/12)","v":0.28867513459481287}]
[null,"SD(RAND) POP",{"$f":"STDEVP(C31:C80)","v":0.29837774935382128}]
[null,"SD(RAND) Sample",{"$f":"STDEV(C31:C80)","v":0.30140704274752428}]
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[null,17,2.6445112217058475E-2]
[null,18,0.15340721797456325]
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[null,"30 Minute TV Show Has Actual Show Time Of",22,"MINUTES"]
[null,"a",18]
[null,"b",26]
[null,"height = f(x) = 1/(b-a) =",{"$f":"1/(C3-C2)","v":0.125}]
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["a","x1",25]
[null,"x2",26]
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["b","x1",21]
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["c","x1",18]
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{"sheet":"(8,9)","index":5,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"(12,14)","index":6,"n_rows":17,"n_cols":8,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
[12]
[null,"z1","z2","operator","Prob",null,"old Functions"]
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[]
[12]
[null,"Prob","z1",null,null,"old Functions"]
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{"sheet":"(17)","index":7,"n_rows":2444,"n_cols":15,"rows_kept":2444,"cut":false,"hidden":false,"merged":[]}
["Mean debt =",15015]
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[null,27090,3.352669177282551E-7,3.352669177282551E-7,"","",""]
[null,27100,3.3205059533677638E-7,3.3205059533677638E-7,"","",""]
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{"sheet":"(21)","index":8,"n_rows":4,"n_cols":6,"rows_kept":4,"cut":false,"hidden":false,"merged":[]}
["Top part of probability under curve = ",0.02]
["Mean =",100]
["SD =",15,null,null,"old function"]
["What score to qualify?",{"$f":"_xlfn.NORM.INV(1-B1,B2,B3)","v":130.80623365947733},null,null,{"$f":"NORMINV(1-B1,B2,B3)","v":130.80623365947733},{"$f":"E4=B4","v":true}]

{"sheet":"(23)","index":9,"n_rows":18,"n_cols":7,"rows_kept":18,"cut":false,"hidden":false,"merged":[]}
["Mean ",80,"minutes"]
["sd",10,"minutes"]
[]
["a"]
["x",60,null,null,null,"Old Functions"]
[{"$f":"\"P(x<=\"&B5&\")\"","v":"P(x<=60)"},{"$f":"_xlfn.NORM.DIST(B5,B1,B2,1)","v":2.2750131948179191E-2},null,null,null,{"$f":"NORMDIST(B5,B1,B2,1)","v":2.2750131948179191E-2},{"$f":"F6=B6","v":true}]
[]
["b"]
["x1",75]
["x2",60]
[{"$f":"\"P(\"&B10&\"<x<\"&B9&\")\"","v":"P(60<x<75)"},{"$f":"_xlfn.NORM.DIST(B9,B1,B2,1)-_xlfn.NORM.DIST(B10,B1,B2,1)","v":0.28578740677780767},null,null,null,{"$f":"NORMDIST(B9,B1,B2,1)-NORMDIST(B10,B1,B2,1)","v":0.28578740677780767},{"$f":"F11=B11","v":true}]
[]
["c"]
["# students =",60]
["Period =",90,"minutes"]
["Probability of not finishing",{"$f":"1-_xlfn.NORM.DIST(B15,B1,B2,1)","v":0.15865525393145696},null,null,null,{"$f":"1-NORMDIST(B15,B1,B2,1)","v":0.15865525393145696},{"$f":"B16=F16","v":true}]
["# students not finish",{"$f":"B14*B16","v":9.5193152358874187},null,null,null,{"$f":"B14*F16","v":9.5193152358874187},true]
["We would expect about 10 students to not finish"]

{"sheet":"(24)","index":10,"n_rows":16,"n_cols":16,"rows_kept":16,"cut":false,"hidden":false,"merged":[]}
["Population distribution of trading volume is approximately Normal"]
[]
["Day","Early Morning Trading Volume (000,000)",null,"a","Sample Mean Point Estimate for Pop Mean",{"$f":"AVERAGE(B4:B16)","v":199.69230769230768},null,null,null,null,null,null,"Check"]
["Day1",214,null,null,"Sample SD Point Estimate for Pop SD",{"$f":"_xlfn.STDEV.S(B4:B16)","v":26.039664025561159},null,null,null,null,null,null,{"$f":"STDEV(B4:B16)","v":26.039664025561159},{"$f":"M4=F4","v":true}]
["Day2",202]
["Day3",174,null,null,"x","operator","Probability","Written Answer",null,"z","Probability",null,"x","z"]
["Day4",163,null,"b",180,"<",{"$f":"_xlfn.NORM.DIST(E7,F3,F4,1)","v":0.22475182649244865},{"$f":"\"Assuming that our point estimates are reliable estimators, we can reasonably say that there is a \"&TEXT(M7,\"0.00%\")&\" chance that on a randomly selected day the early morning trading volume will be less than \"&TEXT(E7*100000,\"#,###\")&\".\"","v":"Assuming that our point estimates are reliable estimators, we can reasonably say that there is a 22.48% chance that on a randomly selected day the early morning trading volume will be less than 18,000,000."},null,{"$f":"(E7-$F$3)/$M$4","v":-0.75624277152643893},{"$f":"_xlfn.NORM.S.DIST(J7,1)","v":0.22475182649244865},null,{"$f":"NORMDIST(E7,$F$3,$M$4,1)","v":0.22475182649244865},{"$f":"NORMSDIST(J7)","v":0.22475182649244865},{"$f":"G7=M7","v":true},{"$f":"N7=K7","v":true}]
["Day5",198,null,"c",230,">",{"$f":"1-_xlfn.NORM.DIST(E8,F3,F4,1)","v":0.12223127873139383},{"$f":"\"Assuming that our point estimates are reliable estimators, we can reasonably say that there is a \"&TEXT(M8,\"0.00%\")&\" chance that on a randomly selected day the early morning trading volume will be more than \"&TEXT(E8*100000,\"#,###\")&\".\"","v":"Assuming that our point estimates are reliable estimators, we can reasonably say that there is a 12.22% chance that on a randomly selected day the early morning trading volume will be more than 23,000,000."},null,{"$f":"(E8-$F$3)/$M$4","v":1.1639048905524112},{"$f":"1-_xlfn.NORM.S.DIST(J8,1)","v":0.12223127873139383},null,{"$f":"1-NORMDIST(E8,$F$3,$M$4,1)","v":0.12223127873139383},{"$f":"1-NORMSDIST(J8)","v":0.12223127873139383},true,true]
["Day6",171,null,null,"prob","operator","X","Written Answer",null,"z","Value",null,"X",{"$f":"K9","v":"Value"}]
["Day7",265,null,"d",0.05,">",{"$f":"_xlfn.NORM.INV(1-E10,F3,F4)","v":242.52374350934971},{"$f":"\"Assuming that our point estimates are reliable estimators, we can reasonably say that \"&ROUND(G10,2)&\" shares would have to be traded to be amongst the busiest \"&TEXT(E10,\"0.00%\")&\".\"","v":"Assuming that our point estimates are reliable estimators, we can reasonably say that 242.52 shares would have to be traded to be amongst the busiest 5.00%."},null,{"$f":"NORMSINV(1-E10)","v":1.6448536269514715},{"$f":"J10*F4+F3","v":242.52374350934971},null,{"$f":"NORMINV(1-E10,F3,M4)","v":242.52374350934971},{"$f":"J10*M4+F3","v":242.52374350934971},{"$f":"G10=M10","v":true},{"$f":"N10=K10","v":true}]
["Day8",212]
["Day9",211]
["Day10",194]
["Day11",201]
["Day12",211]
["Day13",180]

{"sheet":"22 and 41 and 42","index":11,"n_rows":3,"n_cols":1,"rows_kept":3,"cut":false,"hidden":false,"merged":[]}
["No Answers, but try it yourself (similar to problems in Videos)"]
["This Video:"]
["Excel 2010 Statistics 62: Calculating Probabilities & X Values For Bell Normal Distribution (10 Examples)"]

{"sheet":"(28)","index":12,"n_rows":548,"n_cols":12,"rows_kept":548,"cut":false,"hidden":false,"merged":[]}
[null,"Wait Time to get through airport security during peak periods"]
[null,"Mean wait time = ",12.1]
[null,"Assume that distribution is exponential"]
[null,{"$f":"B1&CHAR(10)&\" \"&B2&\" = \"&C2","v":"Wait Time to get through airport security during peak periods\n Mean wait time =  = 12.1"}]
[]
[null,"X1","X2","Operator","P(x)","P(x)","check"]
["a",10,null,"<",{"$f":"\"P(x\"&D7&B7&\")\"","v":"P(x<10)"},{"$f":"_xlfn.EXPON.DIST(B7,1/$C$2,1)","v":0.56239836036108937},{"$f":"1-EXP(1)^(-B7/$C$2)","v":0.56239836036108937}," =EXPON.DIST(B7,1/$C$2,1)",null,null,"or"," =1-EXP(1)^(-B7/$C$2)"]
["b",20,null,">",{"$f":"\"P(x\"&D8&B8&\")\"","v":"P(x>20)"},{"$f":"1-_xlfn.EXPON.DIST(B8,1/$C$2,1)","v":0.19149519501466306},{"$f":"EXP(1)^(-B8/C2)","v":0.19149519501466306}," =1-EXPON.DIST(B8,1/$C$2,1)",null,null,"or"," =EXP(1)^(-B8/C2)"]
["c",10,20,">=",{"$f":"\"P(\"&B9&D9&\" x \"&D9&C9&\")\"","v":"P(10>= x >=20)"},{"$f":"_xlfn.EXPON.DIST(C9,1/C2,1)-_xlfn.EXPON.DIST(B9,1/C2,1)","v":0.24610644462424758},{"$f":"(1-EXP(1)^(-C9/C2))-(1-EXP(1)^(-B9/C2))","v":0.24610644462424758}," =EXPON.DIST(C9,1/C2,1)-EXPON.DIST(B9,1/C2,1)",null,null,"or"," =(1-EXP(1)^(-C9/C2))-(1-EXP(1)^(-B9/C2))"]
["d","Total Time =",30,"mins"]
[null,"Get to gate after through security Check",12]
[null,"Difference",{"$f":"C10-C11","v":18},"<",{"$f":"\"P(x\"&D12&C12&\")\"","v":"P(x<18)"},{"$f":"_xlfn.EXPON.DIST(C12,1/$C$2,1)","v":0.77408654731701398}]
[null,null,null,null,"P(not make) =",{"$f":"1-F12","v":0.22591345268298602}]
[null,null,"height",null,null,null,null,null,null,null,null,"check"]
[null,"x","f(x)",{"$f":"\"X\"&D7&B7","v":"X<10"},{"$f":"\"X\"&D8&B8","v":"X>20"},null,null,null,null,null,null,"f(x)"]
[null,0,{"$f":"_xlfn.EXPON.DIST(B16,1/$C$2,0\n)","v":8.2644628099173556E-2},{"$f":"IF($B16<$B$7,$C16,\"\")","v":8.2644628099173556E-2},{"$f":"IF($B16>$B$8,$C16,\"\")","v":""},null,null,null,null,null,null,{"$f":"1/$C$2*EXP(1)^(-B16/$C$2)","v":8.2644628099173556E-2}]
[null,{"$f":"B16+0.1","v":0.1},{"$f":"_xlfn.EXPON.DIST(B17,1/$C$2,0\n)","v":8.1964429254373541E-2},{"$f":"IF(B17<$B$7,C17,\"\")","v":8.1964429254373541E-2},{"$f":"IF($B17>$B$8,$C17,\"\")","v":""},null,null,null,null,null,null,{"$f":"1/$C$2*EXP(1)^(-B17/$C$2)","v":8.1964429254373541E-2}]
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[null,0.6,7.8646493862383288E-2,7.8646493862383288E-2,"",null,null,null,null,null,null,7.8646493862383302E-2]
[null,0.7,7.7999201285682829E-2,7.7999201285682829E-2,"",null,null,null,null,null,null,7.7999201285682843E-2]
[null,0.79999999999999993,7.7357236189703707E-2,7.7357236189703707E-2,"",null,null,null,null,null,null,7.7357236189703707E-2]
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[null,1.0999999999999999,7.5462869114236553E-2,7.5462869114236553E-2,"",null,null,null,null,null,null,7.5462869114236553E-2]
[null,1.2,7.4841779061835298E-2,7.4841779061835298E-2,"",null,null,null,null,null,null,7.4841779061835298E-2]
[null,1.3,7.4225800832741565E-2,7.4225800832741565E-2,"",null,null,null,null,null,null,7.4225800832741565E-2]
[null,1.4000000000000001,7.3614892354574052E-2,7.3614892354574052E-2,"",null,null,null,null,null,null,7.3614892354574052E-2]
[null,1.5000000000000002,7.3009011901224177E-2,7.3009011901224177E-2,"",null,null,null,null,null,null,7.3009011901224163E-2]
[null,1.6000000000000003,7.2408118090006204E-2,7.2408118090006204E-2,"",null,null,null,null,null,null,7.2408118090006204E-2]
[null,1.7000000000000004,7.1812169878830726E-2,7.1812169878830726E-2,"",null,null,null,null,null,null,7.1812169878830739E-2]
[null,1.8000000000000005,7.1221126563401349E-2,7.1221126563401349E-2,"",null,null,null,null,null,null,7.1221126563401363E-2]
[null,1.9000000000000006,7.0634947774434603E-2,7.0634947774434603E-2,"",null,null,null,null,null,null,7.0634947774434589E-2]
[null,2.0000000000000004,7.0053593474902573E-2,7.0053593474902573E-2,"",null,null,null,null,null,null,7.0053593474902573E-2]
[null,2.1000000000000005,6.9477023957298364E-2,6.9477023957298364E-2,"",null,null,null,null,null,null,6.9477023957298364E-2]
[null,2.2000000000000006,6.8905199840924011E-2,6.8905199840924011E-2,"",null,null,null,null,null,null,6.8905199840924011E-2]
[null,2.3000000000000007,6.8338082069200626E-2,6.8338082069200626E-2,"",null,null,null,null,null,null,6.8338082069200626E-2]
[null,2.4000000000000008,6.7775631907000866E-2,6.7775631907000866E-2,"",null,null,null,null,null,null,6.7775631907000866E-2]
[null,2.5000000000000009,6.7217810938003192E-2,6.7217810938003192E-2,"",null,null,null,null,null,null,6.7217810938003206E-2]
[null,2.600000000000001,6.6664581062068004E-2,6.6664581062068004E-2,"",null,null,null,null,null,null,6.6664581062068004E-2]
[null,2.7000000000000011,6.6115904492635311E-2,6.6115904492635311E-2,"",null,null,null,null,null,null,6.6115904492635311E-2]
[null,2.8000000000000012,6.5571743754143832E-2,6.5571743754143832E-2,"",null,null,null,null,null,null,6.5571743754143846E-2]
[null,2.9000000000000012,6.5032061679471426E-2,6.5032061679471426E-2,"",null,null,null,null,null,null,6.5032061679471426E-2]
[null,3.0000000000000013,6.4496821407396418E-2,6.4496821407396418E-2,"",null,null,null,null,null,null,6.4496821407396418E-2]
[null,3.1000000000000014,6.3965986380079942E-2,6.3965986380079942E-2,"",null,null,null,null,null,null,6.3965986380079942E-2]
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[null,3.4000000000000017,6.2399551686743111E-2,6.2399551686743111E-2,"",null,null,null,null,null,null,6.2399551686743118E-2]
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{"sheet":"(29)","index":13,"n_rows":628,"n_cols":10,"rows_kept":628,"cut":false,"hidden":false,"merged":[]}
[null,"Follows Exponential Distribution",null,null,null,{"$f":"B1&CHAR(10)&B2&\" = \"&C2&\" \"&D2","v":"Follows Exponential Distribution\nAverage time between arrivals at intersection = 12 seconds"}]
[null,"Average time between arrivals at intersection",12,"seconds"]
[]
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{"sheet":"(32)","index":14,"n_rows":15,"n_cols":4,"rows_kept":15,"cut":false,"hidden":false,"merged":[]}
[null,"interruptions at work",5.5]
[null,"Time interval",1,"hour"]
[]
[null,"New Mean",{"$f":"C1*C6","v":1.375},"# interuptions"]
[null,"New Time",15,"minutes"]
[null,"New Time",{"$f":"C5/60","v":0.25},"hours"]
[]
["b","Poisson"]
[null,"x",0,{"$f":"\"# interruptions per \"&C5&\" \"&D5","v":"# interruptions per 15 minutes"}]
[null,{"$f":"\"P(x=\"&C9&\")\"","v":"P(x=0)"},{"$f":"_xlfn.POISSON.DIST(C9,C4,0)","v":0.25283959580474646}]
[]
["c","Exponetial"]
[null,"Mean",{"$f":"C5/C4","v":10.909090909090908},"Time (minutes) between interuptions"]
[null,"x",10,"minutes between interuptions"]
[null,{"$f":"\"P(x<=\"&C14&\")\"","v":"P(x<=10)"},{"$f":"_xlfn.EXPON.DIST(C14,1/C13,1)","v":0.60015034565515268}]

{"sheet":"(32.1)","index":15,"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 Exponetial 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*E11","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$14,1)","v":0.60015034565515268}]
[null,{"$f":"\"P(x<\"&$D$23&\")\"","v":"P(x<15)"},{"$f":"1-EXP(1)^(-D18/$C$14)","v":0.60015034565515268},null,null,null,null,null,"1 - e^(-x/mu)"]
["P(not interruptions during 15 minute)"]
[null,null,"x1","x2"]
[null,null,0,15,"minutes"]
[null,{"$f":"\"P(x>\"&$D$23&\")\"","v":"P(x>15)"},{"$f":"1-_xlfn.EXPON.DIST(D23,1/$C$14,1)","v":0.25283959580474646}]
[null,{"$f":"\"P(x>\"&$D$23&\")\"","v":"P(x>15)"},{"$f":"EXP(1)^(-D23/$C$14)","v":0.25283959580474652}]
[]
["x (min)","f(x)",{"$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$14,1),\"0.00%\")","v":"P(x>15) = 25.28%"},"."]
[0,{"$f":"EXPONDIST(A28,1/$C$14,0)","v":9.166666666666666E-2},{"$f":"IF(A28<$D$18,B28,\"\")","v":9.166666666666666E-2},{"$f":"IF(A28>$D$23,B28,\"\")","v":""}]
[{"$f":"A28+0.1","v":0.1},{"$f":"EXPONDIST(A29,1/$C$14,0)","v":9.0830228421176426E-2},{"$f":"IF(A29<$D$18,B29,\"\")","v":9.0830228421176426E-2},{"$f":"IF(A29>$D$23,B29,\"\")","v":""}]
[{"$f":"A29+0.1","v":0.2},9.0001422491379129E-2,9.0001422491379129E-2,""]
[0.30000000000000004,8.9180179234066612E-2,8.9180179234066612E-2,""]
[0.4,8.8366429641509731E-2,8.8366429641509731E-2,""]
[0.5,8.7560105335659763E-2,8.7560105335659763E-2,""]
[0.6,8.6761138562402682E-2,8.6761138562402682E-2,""]
[0.7,8.5969462185865902E-2,8.5969462185865902E-2,""]
[0.79999999999999993,8.5185009682776994E-2,8.5185009682776994E-2,""]
[0.89999999999999991,8.4407715136873743E-2,8.4407715136873743E-2,""]
[0.99999999999999989,8.3637513233365463E-2,8.3637513233365463E-2,""]
[1.0999999999999999,8.2874339253444562E-2,8.2874339253444562E-2,""]
[1.2,8.2118129068848411E-2,8.2118129068848411E-2,""]
[1.3,8.1368819136470733E-2,8.1368819136470733E-2,""]
[1.4000000000000001,8.0626346493022125E-2,8.0626346493022125E-2,""]
[1.5000000000000002,7.989064874973946E-2,7.989064874973946E-2,""]
[1.6000000000000003,7.9161664087143369E-2,7.9161664087143369E-2,""]
[1.7000000000000004,7.8439331249843688E-2,7.8439331249843688E-2,""]
[1.8000000000000005,7.7723589541392274E-2,7.7723589541392274E-2,""]
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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]
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[47.300000000000402,1.200004702654579E-3,"",1.200004702654579E-3]
[47.400000000000404,1.1890549227120137E-3,"",1.1890549227120137E-3]
[47.500000000000405,1.1782050571118893E-3,"",1.1782050571118893E-3]
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[47.700000000000408,1.1568014304720723E-3,"",1.1568014304720723E-3]
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[49.900000000000439,9.4553170618674374E-4,"",9.4553170618674374E-4]
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["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":"'(32.1)'!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"]
[{"$f":"\"Mean for Exponetial Distribution = \"&B6&\" = \"&C6&\" \"&D6&\" \"&E6&\" \"&F6","v":"Mean for Exponetial Distribution = Time between interruptions = 0.181818181818182 hours  "},null,null,null,null,null,null,null,null,null,null,null,"The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval",null,null,null,null,"Excel function: EXPONDIST"]
["x","Time between interruptions",{"$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,"EXPONDIST(x,1/mu, (0 = exact, 1 = cumulative))"]
[null,null,{"$f":"C6*$E$4","v":10.90909090909091},"minutes",null,null,null,null,null,null,null,null,"Mean = Var"]
[null,null,null,null,null,null,null,null,null,null,null,null,"Excel function: POISSON"]
["P(no interruptions during 15 minute period 0 to 15)",null,null,null,null,null,null,null,null,null,null,null,"POISSON(x,mean,cumulative (0 = exact, 1 = cumulative))"]
[]
[null,null,"x1","x2"]
[null,null,0,15,"minutes"]
[null,{"$f":"\"P(x<\"&$D$12&\")\"","v":"P(x<15)"},{"$f":"1-_xlfn.EXPON.DIST(D12,1/C7,1)","v":0.25283959580474646},"Exponential, x = time between occurrences"]
[]
[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,C17,0)","v":0.25283959580474646},"Poisson, x = # of occurrences"]

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