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{"sheet":"Dick's Hamburger Data","index":0,"n_rows":1316,"n_cols":14,"rows_kept":1316,"cut":false,"hidden":false,"merged":[]}
["Data collected: Number of Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period.",null,null,null,null,null,null,null,null,null,null,null,null,"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88"]
["Discrete Variable = X = Number of Arrivals in 1 min period during Sat. noon lunch rush (noon to 1 PM)"]
[]
["Properties (Requirements) of a Poisson Experiment:"]
["1) The probability of an occurrence (success) is the same for all equal-size intervals"]
["2) The number of occurrences (successes) that occur in any interval is independent of the number of occurrences (successes) in any other interval"]
["3) The probability of an occurrence (success) is proportional to the size of the interval (if interval doubles, proportion doubles, mean doubles)."]
["4) Mean = Variance (observed from calculations made off of source data)"]
["5) As with all our distributions, actual Relative Frequency Pattern from past data fits the \"Poisson Pattern\""]
[]
["X = Arrivals During 1 min",null,"X = Arrivals During 1 min","Frequency","P(X) Relative Frequency",null,"Mean",{"$f":"SUMPRODUCT(C12:C26,E12:E26)","v":3.8796934865900377},null,"X = Arrivals During 1 min","P(X) POISSON Function",null,"Mean"]
[0,null,0,{"$f":"COUNTIFS($A$12:$A$1316,C12)","v":28},{"$f":"D12/$D$27","v":2.1455938697318006E-2},null,"Variance",{"$f":"SUMPRODUCT((C12:C26-H11)^2,E12:E26)","v":3.7518098677353535},null,0,null,null,"Variance"]
[0,null,1,102,7.8160919540229884E-2,null,"SD",{"$f":"SQRT(H12)","v":1.9369589225730508},null,1]
[0,null,2,191,0.14636015325670498,null,null,null,null,2]
[0,null,3,263,0.20153256704980843,null,null,null,null,3]
[0,null,4,266,0.20383141762452106,null,null,null,null,4]
[0,null,5,204,0.15632183908045977,null,null,null,null,5]
[0,null,6,136,0.10421455938697317,null,null,null,null,6]
[0,null,7,70,5.3639846743295021E-2,null,null,null,null,7]
[0,null,8,22,1.6858237547892719E-2,null,null,null,null,8]
[0,null,9,14,1.0727969348659003E-2,null,null,null,null,9]
[0,null,10,5,3.8314176245210726E-3,null,null,null,null,10]
[0,null,11,2,1.5325670498084292E-3,null,null,null,null,11]
[0,null,12,1,7.6628352490421458E-4,null,null,null,null,12]
[0,null,13,0,0,null,null,null,null,13]
[0,null,14,1,7.6628352490421458E-4,null,null,null,null,14]
[0,null,"Total",{"$f":"SUM(D12:D26)","v":1305},{"$f":"SUM(E12:E26)","v":1},null,null,null,null,15]
[0,null,null,null,null,null,null,null,null,16]
[0,null,null,null,null,null,null,null,null,17]
[0,null,null,null,null,null,null,null,null,18]
[0,null,null,null,null,null,null,null,null,19]
[0,null,null,null,null,null,null,null,null,20]
[0,null,null,null,null,null,null,null,null,21]
[0,null,null,null,null,null,null,null,null,22]
[0,null,null,null,null,null,null,null,null,23]
[0,null,null,null,null,null,null,null,null,24]
[0,null,null,null,null,null,null,null,null,25]
[0,null,null,null,null,null,null,null,null,26]
[0,null,null,null,null,null,null,null,null,27]
[1,null,null,null,null,null,null,null,null,28]
[1,null,null,null,null,null,null,null,null,29]
[1,null,null,null,null,null,null,null,null,"Total"]
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{"sheet":"Dick's Hamburger Data (an)","index":1,"n_rows":1316,"n_cols":14,"rows_kept":1316,"cut":false,"hidden":false,"merged":[]}
["Data collected: Number of Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period.",null,null,null,null,null,null,null,null,null,null,null,null,"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88"]
["Discrete Variable = X = Number of Arrivals in 1 min period during Sat. noon lunch rush (noon to 1 PM)"]
[]
["Properties (Requirements) of a Poisson Experiment:"]
["1) The probability of an occurrence (success) is the same for all equal-size intervals"]
["2) The number of occurrences (successes) that occur in any interval is independent of the number of occurrences (successes) in any other interval"]
["3) The probability of an occurrence (success) is proportional to the size of the interval (if interval doubles, proportion doubles, mean doubles)."]
["4) Mean = Variance (observed from calculations made off of source data)"]
["5) As with all our distributions, actual Relative Frequency Pattern from past data fits the \"Poisson Pattern\""]
[]
["X = Arrivals During 1 min",null,"X = Arrivals During 1 min","Frequency","P(X) Relative Frequency",null,"Mean",{"$f":"SUMPRODUCT(C12:C26,E12:E26)","v":3.8796934865900377},null,"X = Arrivals During 1 min","P(X) POISSON Function",null,"Mean",{"$f":"SUMPRODUCT(J12:J41,K12:K41)","v":3.8796934865900377}]
[0,null,0,{"$f":"COUNTIFS($A$12:$A$1316,C12)","v":28},{"$f":"D12/$D$27","v":2.1455938697318006E-2},null,"Variance",{"$f":"SUMPRODUCT((C12:C26-H11)^2,E12:E26)","v":3.7518098677353535},null,0,{"$f":"_xlfn.POISSON.DIST(J12,$H$11,0)","v":2.0657155906734039E-2},null,"Variance",{"$f":"SUMPRODUCT((J12:J41-N11)^2,K12:K41)","v":3.8796934865900115}]
[0,null,1,102,7.8160919540229884E-2,null,"SD",{"$f":"SQRT(H12)","v":1.9369589225730508},null,1,{"$f":"_xlfn.POISSON.DIST(J13,$H$11,0)","v":8.0143433222830962E-2}]
[0,null,2,191,0.14636015325670498,null,null,null,null,2,0.15546597793379047]
[0,null,3,263,0.20153256704980843,null,null,null,null,3,0.20105344732535915]
[0,null,4,266,0.20383141762452106,null,null,null,null,4,0.19500643751116731]
[0,null,5,204,0.15632183908045977,null,null,null,null,5,0.15131304109104057]
[0,null,6,136,0.10421455938697317,null,null,null,null,6,9.7841369992840196E-2]
[0,null,7,70,5.3639846743295021E-2,null,null,null,null,7,5.422778941146681E-2]
[0,null,8,22,1.6858237547892719E-2,null,null,null,null,8,2.629840017148051E-2]
[0,null,9,14,1.0727969348659003E-2,null,null,null,null,9,1.1336636872559043E-2]
[0,null,10,5,3.8314176245210726E-3,null,null,null,null,10,4.3982676234303724E-3]
[0,null,11,2,1.5325670498084292E-3,null,null,null,null,11,1.5512663864456972E-3]
[0,null,12,1,7.6628352490421458E-4,null,null,null,null,12,5.0153650795495405E-4]
[0,null,13,0,0,null,null,null,null,13,1.4967753255384184E-4]
[0,null,14,1,7.6628352490421458E-4,null,null,null,null,14,4.1478782009857794E-5]
[0,null,"Total",{"$f":"SUM(D12:D26)","v":1305},{"$f":"SUM(E12:E26)","v":1},null,null,null,null,15,1.0728330693022219E-5]
[0,null,null,null,null,null,null,null,null,16,2.6014146694813857E-6]
[0,null,null,null,null,null,null,null,null,17,5.9368773818274939E-7]
[0,null,null,null,null,null,null,null,null,18,1.279625806053326E-7]
[0,null,null,null,null,null,null,null,null,19,2.6129241605355779E-8]
[0,null,null,null,null,null,null,null,null,20,5.0686724232918323E-9]
[0,null,null,null,null,null,null,null,null,21,9.3642358982398654E-10]
[0,null,null,null,null,null,null,null,null,22,1.6513802282406363E-10]
[0,null,null,null,null,null,null,null,null,23,2.7855865719081618E-11]
[0,null,null,null,null,null,null,null,null,24,4.503009199735325E-12]
[0,null,null,null,null,null,null,null,null,25,6.9881181849072024E-13]
[0,null,null,null,null,null,null,null,null,26,1.0427598694425402E-13]
[0,null,null,null,null,null,null,null,null,27,1.4983661753902525E-14]
[1,null,null,null,null,null,null,null,null,28,2.0761433897101461E-15]
[1,null,null,null,null,null,null,null,null,29,2.7775172366501524E-16]
[1,null,null,null,null,null,null,null,null,"Total",{"$f":"SUM(K12:K41)","v":1}]
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{"sheet":"POISSON.DIST","index":2,"n_rows":179,"n_cols":14,"rows_kept":179,"cut":false,"hidden":false,"merged":[]}
["POISSON Discrete Probability Distribution"]
["Used to estimate the number of occurrences (successes) over specified interval of time or space"]
["Whereas Binomial counts number of successes over a specified number of trials,"]
["Poisson counts number of occurances (successes) over specified  interval of time or space"]
["Good for estimating the probabilities of:"]
["1) Line waiting situations, where you know the mean number of arrivals over a certain time interval"]
["Example: From past data we know that the mean number of arrivals at the Dick's Hamburger Restaurant at Sat. Lunch is 3.88 people/minute."]
["With this information we can make estimates of the probability that a certain number of people will show up over this interval"]
["2) Distance of road or pipe intervals, where you know the mean number of repairs over a certain distance interval"]
[{"$f":"\"Example: From past data we know that the mean number of water line breaks is \"&B94&\" per 100 miles of pipe in Richmond, CA.\"","v":"Example: From past data we know that the mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."}]
["With this information we can make estimates of the probability that a certain number of water line breaks will occur over a 100 mile stretch"]
["THE most amazing thing about this distribution is that the only number you need to make your probability calculations is the mean."]
["Properties (Requirements) of a Poisson Experiment:"]
["1) The probability of an occurrence (success) is the same for all equal-size intervals"]
["2) The number of occurrences (successes) that occur in any interval is independent of the number of occurrences (successes) in any other interval"]
["3) The probability of an occurrence (success) is proportional to the size of the interval (if interval doubles, proportion doubles, mean doubles)."]
["4) Mean = Variance (observed from calculations made off of source data)"]
["5) As with all our distributions, actual Relative Frequency Pattern from past data fits the \"Poisson Pattern\""]
["f(x) = P(x) = the probability of x occurrences in an interval = height of column when you plot column chart."]
["Discrete Random Variable = X = Number of occurrences over a specified interval of time or space."]
["No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gets quite small."]
["Mean = µ = Calculated from past data"]
["e = constant = 2.71828 = =EXP(1) in Excel"]
["In Excel use: POISSON.DIST(x,mean,cumulative)"]
["x = Number of occurrences over a specified interval of time or space = Discrete Random Variable"]
["mean = µ = Calculated from past data"]
["cumulative = 0 for exactly x OR 1 for less than or equal to x"]
[]
["Example 1:"]
["From past data we know that the mean number of arrivals at the Dick's Hamburger Restaurant at Sat. Lunch is 3.88 people/minute.",null,null,null,null,null,null,null,null,null,null,"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88"]
["Assume:  The probability of a person arriving is the same for all equal-size intervals"]
["Assume: The number of people arriving in any interval is independent of the number of people arriving in any other interval"]
["Goal: calculate the probability that 0 perople will arrive in 1 minute. 3 to 5 people in 1 minute?"]
[]
["Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 minute"]
["Expected Value = µ =",3.88,"people arriving/minute"]
["X",0,null,null,null,null,null,"X","P(x)"]
[{"$f":"\"P(\"&B37&\")\"","v":"P(0)"},null,null,{"$f":"B36^B37*EXP(1)^-B36/FACT(B37)","v":2.0650825181712566E-2},null,null,null,0,{"$f":"_xlfn.POISSON.DIST(H38,$B$36,0)","v":2.0650825181712566E-2}]
["X",3]
["X",5]
[{"$f":"\"P(\"&$B$39&\"<= Arrivals in 1 minute  <=\"&$B$40&\")\"","v":"P(3<= Arrivals in 1 minute  <=5)"}]
["Expected Value = µ =",null,0.5,"minutes"]
["X",2]
[{"$f":"\"P(\"&B43&\" Arrivals in \"&TEXT(C42,\"?/?\")&\" min)\"","v":"P(2 Arrivals in 1/2 min)"}]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Example 2:"]
["From past data we know that the mean number of arrivals for accoutning tutoring is 3 per hour during the morning shift"]
["Assume:  The probability of a person arriving is the same for all equal-size intervals"]
["Assume: The number of people arriving in any interval is independent of the number of people arriving in any other interval"]
["Goal: calculate the probability that 5 people will arrive in 1 hour"]
[]
["Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 hour"]
["Expected Value = µ =",3,"people arriving/hour"]
["X",5]
[{"$f":"\"P(\"&B79&\")\"","v":"P(5)"},null,null,{"$f":"B78^B79*EXP(1)^-B78/FACT(B79)","v":0.10081881344492451}]
[]
[]
[]
[]
[]
["Example 3:"]
[{"$f":"\"From past data we know that the mean number of water line breaks is \"&B94&\" per 100 miles of pipe in Richmond, CA.\"","v":"From past data we know that the mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Mean number of water line breaks is \"&B94&\" per 100 miles of pipe in Richmond, CA.\"","v":"Mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."}]
["With this information we can make estimates of the probability that a certain number of water line breaks will occur over a 100 mile stretch in Richmond, CA."]
["Assume:  The probability of a water breaks is the same for all equal-size intervals"]
["Assume: The number of water breaks in any interval is independent of the number of water breaks in any other interval"]
[{"$f":"\"Goal: calculate the probability that \"&B95&\" or more breaks will occur over a 100 mile stretch of pipe.\"","v":"Goal: calculate the probability that 30 or more breaks will occur over a 100 mile stretch of pipe."}]
[]
["Define Random Discrete Variable = x = ",null,"x = Number of water breaks in 100 miles of pipe"]
["Expected Value = µ =",25,"water breaks/100 miles"]
["X",30]
[{"$f":"\"P(x>=\"&$B$95&\")\"","v":"P(x>=30)"}]
[{"$f":"\"P(x>=\"&$B$95&\")\"","v":"P(x>=30)"}]
[]
["X",10]
[{"$f":"\"P(x<\"&$B$99&\")\"","v":"P(x<10)"}]
[{"$f":"\"P(x<\"&$B$99&\")\"","v":"P(x<10)"}]
[]
["X","P(x)"]
[0]
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
[55]
[56]
[57]
[58]
[59]
[60]
[61]
[62]
[63]
[64]
[65]
[66]
[67]
[68]
[69]
[70]
[71]
[72]
[73]
[74]
["Total"]

{"sheet":"POISSON.DIST (an)","index":3,"n_rows":179,"n_cols":14,"rows_kept":179,"cut":false,"hidden":false,"merged":[]}
["POISSON Discrete Probability Distribution"]
["Used to estimate the number of occurrences (successes) over specified interval of time or space"]
["Whereas Binomial counts number of successes over a specified number of trials,"]
["Poisson counts number of occurances (successes) over specified  interval of time or space"]
["Good for estimating the probabilities of:"]
["1) Line waiting situations, where you know the mean number of arrivals over a certain time interval"]
["Example: From past data we know that the mean number of arrivals at the Dick's Hamburger Restaurant at Sat. Lunch is 3.88 people/minute."]
["With this information we can make estimates of the probability that a certain number of people will show up over this interval"]
["2) Distance of road or pipe intervals, where you know the mean number of repairs over a certain distance interval"]
[{"$f":"\"Example: From past data we know that the mean number of water line breaks is \"&B94&\" per 100 miles of pipe in Richmond, CA.\"","v":"Example: From past data we know that the mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."}]
["With this information we can make estimates of the probability that a certain number of water line breaks will occur over a 100 mile stretch"]
["THE most amazing thing about this distribution is that the only number you need to make your probability calculations is the mean."]
["Properties (Requirements) of a Poisson Experiment:"]
["1) The probability of an occurrence (success) is the same for all equal-size intervals"]
["2) The number of occurrences (successes) that occur in any interval is independent of the number of occurrences (successes) in any other interval"]
["3) The probability of an occurrence (success) is proportional to the size of the interval (if interval doubles, proportion doubles, mean doubles)."]
["4) Mean = Variance (observed from calculations made off of source data)"]
["5) As with all our distributions, actual Relative Frequency Pattern from past data fits the \"Poisson Pattern\""]
["f(x) = P(x) = the probability of x occurrences in an interval = height of column when you plot column chart."]
["Discrete Random Variable = X = Number of occurrences over a specified interval of time or space."]
["No upper limit for X: 0,1,2,3… , but as x increases past the mean, the probability decreases and gets quite small."]
["Mean = µ = Calculated from past data"]
["e = constant = 2.71828 = =EXP(1) in Excel"]
["In Excel use: POISSON.DIST(x,mean,cumulative)"]
["x = Number of occurrences over a specified interval of time or space = Discrete Random Variable"]
["mean = µ = Calculated from past data"]
["cumulative = 0 for exactly x OR 1 for less than or equal to x"]
[]
["Example 1:"]
["From past data we know that the mean number of arrivals at the Dick's Hamburger Restaurant at Sat. Lunch is 3.88 people/minute.",null,null,null,null,null,null,null,null,null,null,"Arrivals to Dick's Hamburgers at 45th Ave in Seattle at Saturday noon lunch during a 1-minute period. Mean = 3.88"]
["Assume:  The probability of a person arriving is the same for all equal-size intervals"]
["Assume: The number of people arriving in any interval is independent of the number of people arriving in any other interval"]
["Goal: calculate the probability that 0 perople will arrive in 1 minute. 3 to 5 people in 1 minute?"]
[]
["Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 minute"]
["Expected Value = µ =",3.88,"people arriving/minute"]
["X",0,null,null,null,null,null,"X","P(x)"]
[{"$f":"\"P(\"&B37&\")\"","v":"P(0)"},{"$f":"_xlfn.POISSON.DIST(B37,B36,0)","v":2.0650825181712566E-2},null,{"$f":"B36^B37*EXP(1)^-B36/FACT(B37)","v":2.0650825181712566E-2},null,null,null,0,{"$f":"_xlfn.POISSON.DIST(H38,$B$36,0)","v":2.0650825181712566E-2}]
["X",3,null,null,null,null,null,1,{"$f":"_xlfn.POISSON.DIST(H39,$B$36,0)","v":8.0125201705044752E-2}]
["X",5,null,null,null,null,null,2,0.1554428913077868]
[{"$f":"\"P(\"&$B$39&\"<= Arrivals in 1 minute  <=\"&$B$40&\")\"","v":"P(3<= Arrivals in 1 minute  <=5)"},{"$f":"_xlfn.POISSON.DIST(B40,B36,1)-_xlfn.POISSON.DIST(B39-1,B36,1)","v":0.54737419326785508},null,null,null,null,null,3,0.20103947275807099]
["Expected Value = µ =",{"$f":"B36/2","v":1.94},0.5,"minutes",null,null,null,4,0.19500828857532884]
["X",2,null,null,null,null,null,5,0.15132643193445516]
[{"$f":"\"P(\"&B43&\" Arrivals in \"&TEXT(C42,\"?/?\")&\" min)\"","v":"P(2 Arrivals in 1/2 min)"},{"$f":"_xlfn.POISSON.DIST(B43,B42,0)","v":0.27042209269168144},null,null,null,null,null,6,9.7857759317614312E-2]
[null,null,null,null,null,null,null,7,5.4241158021763422E-2]
[null,null,null,null,null,null,null,8,2.6306961640555224E-2]
[null,null,null,null,null,null,null,9,1.134122346281714E-2]
[null,null,null,null,null,null,null,10,4.400394703573055E-3]
[null,null,null,null,null,null,null,11,1.5521392227148608E-3]
[null,null,null,null,null,null,null,12,5.0185834867780407E-4]
[null,null,null,null,null,null,null,13,1.4978541483614462E-4]
[null,null,null,null,null,null,null,14,4.1511957826017288E-5]
[null,null,null,null,null,null,null,15,1.0737759757663123E-5]
[null,null,null,null,null,null,null,16,2.6039067412333054E-6]
[null,null,null,null,null,null,null,17,5.943034209403063E-7]
[null,null,null,null,null,null,null,18,1.2810540406935535E-7]
[null,null,null,null,null,null,null,19,2.61604719888999E-8]
[null,null,null,null,null,null,null,20,5.0751315658465849E-9]
[null,null,null,null,null,null,null,21,9.3769097502308185E-10]
[null,null,null,null,null,null,null,22,1.6537459014043502E-10]
[null,null,null,null,null,null,null,23,2.7897974336734243E-11]
[null,null,null,null,null,null,null,24,4.5101725177720354E-12]
[null,null,null,null,null,null,null,25,6.9997877475821791E-13]
[null,null,null,null,null,null,null,26,1.0445837100238E-13]
[null,null,null,null,null,null,null,27,1.5011054795897582E-14]
[null,null,null,null,null,null,null,28,2.0801033074315417E-15]
[null,null,null,null,null,null,null,29,2.7830347699428757E-16]
[null,null,null,null,null,null,null,30,3.599391635792812E-17]
[null,null,null,null,null,null,null,"Total",{"$f":"SUM(I38:I68)","v":1}]
[]
["Example 2:"]
["From past data we know that the mean number of arrivals for accoutning tutoring is 3 per hour during the morning shift"]
["Assume:  The probability of a person arriving is the same for all equal-size intervals"]
["Assume: The number of people arriving in any interval is independent of the number of people arriving in any other interval"]
["Goal: calculate the probability that 5 people will arrive in 1 hour"]
[]
["Define Random Discrete Variable = x = ",null,"x = Number Arrivals during 1 hour"]
["Expected Value = µ =",3,"people arriving/hour"]
["X",5]
[{"$f":"\"P(\"&B79&\")\"","v":"P(5)"},{"$f":"_xlfn.POISSON.DIST(B79,B78,0)","v":0.10081881344492449},null,{"$f":"B78^B79*EXP(1)^-B78/FACT(B79)","v":0.10081881344492451}]
[]
[]
[]
[]
[]
["Example 3:"]
[{"$f":"\"From past data we know that the mean number of water line breaks is \"&B94&\" per 100 miles of pipe in Richmond, CA.\"","v":"From past data we know that the mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."},null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"\"Mean number of water line breaks is \"&B94&\" per 100 miles of pipe in Richmond, CA.\"","v":"Mean number of water line breaks is 25 per 100 miles of pipe in Richmond, CA."}]
["With this information we can make estimates of the probability that a certain number of water line breaks will occur over a 100 mile stretch in Richmond, CA."]
["Assume:  The probability of a water breaks is the same for all equal-size intervals"]
["Assume: The number of water breaks in any interval is independent of the number of water breaks in any other interval"]
[{"$f":"\"Goal: calculate the probability that \"&B95&\" or more breaks will occur over a 100 mile stretch of pipe.\"","v":"Goal: calculate the probability that 30 or more breaks will occur over a 100 mile stretch of pipe."}]
[]
["Define Random Discrete Variable = x = ",null,"x = Number of water breaks in 100 miles of pipe"]
["Expected Value = µ =",25,"water breaks/100 miles"]
["X",30]
[{"$f":"\"P(x>=\"&$B$95&\")\"","v":"P(x>=30)"},{"$f":"1-_xlfn.POISSON.DIST(B95-1,B94,1)","v":0.18210391597745512}]
[{"$f":"\"P(x>=\"&$B$95&\")\"","v":"P(x>=30)"},{"$f":"SUM(B134:B178)","v":0.18210391597745457}]
[]
["X",10]
[{"$f":"\"P(x<\"&$B$99&\")\"","v":"P(x<10)"},{"$f":"_xlfn.POISSON.DIST(B99-1,B94,1)","v":2.2147663824878362E-4}]
[{"$f":"\"P(x<\"&$B$99&\")\"","v":"P(x<10)"},{"$f":"SUM(B104:B113)","v":2.2147663824878357E-4}]
[]
["X","P(x)"]
[0,{"$f":"_xlfn.POISSON.DIST(A104,$B$94,0)","v":1.3887943864964021E-11}]
[1,{"$f":"_xlfn.POISSON.DIST(A105,$B$94,0)","v":3.4719859662410047E-10}]
[2,4.3399824578012608E-9]
[3,3.6166520481677125E-8]
[4,2.2604075301048233E-7]
[5,1.1302037650524102E-6]
[6,4.7091823543850467E-6]
[7,1.6818508408517987E-5]
[8,5.2557838776618804E-5]
[9,1.4599399660171887E-4]
[10,3.6498499150429664E-4]
[11,8.29511344327948E-4]
[12,1.7281486340165607E-3]
[13,3.3233627577241454E-3]
[14,5.934576353078834E-3]
[15,9.8909605884647447E-3]
[16,1.5454625919476139E-2]
[17,2.2727391058053149E-2]
[18,3.1565820913962726E-2]
[19,4.1533974886793022E-2]
[20,5.1917468608491307E-2]
[21,6.1806510248203946E-2]
[22,7.0234670736595409E-2]
[23,7.6342033409342827E-2]
[24,7.9522951468065442E-2]
[25,7.9522951468065442E-2]
[26,7.6464376411601379E-2]
[27,7.0800348529260551E-2]
[28,6.3214596901125505E-2]
[29,5.4495342156142643E-2]
[30,4.5412785130118899E-2]
[31,3.6623213814611991E-2]
[32,2.8611885792665631E-2]
[33,2.1675671055049736E-2]
[34,1.5937993422830674E-2]
[35,1.1384281016307642E-2]
[36,7.905750705769184E-3]
[37,5.3417234498440488E-3]
[38,3.514291743318449E-3]
[39,2.2527511175118192E-3]
[40,1.4079694484448889E-3]
[41,8.5851795636883779E-4]
[42,5.1102259307668864E-4]
[43,2.9710615876551576E-4]
[44,1.6881031748040677E-4]
[45,9.3783509711336947E-5]
[46,5.0969298756161431E-5]
[47,2.7111329125617976E-5]
[48,1.4120483919592659E-5]
[49,7.2043285304044512E-6]
[50,3.6021642652021993E-6]
[51,1.7657667966677478E-6]
[52,8.4892634455180066E-7]
[53,4.0043695497726195E-7]
[54,1.8538747915613944E-7]
[55,8.426703598006342E-8]
[56,3.7619212491099991E-8]
[57,1.6499654601359681E-8]
[58,7.1119200867930007E-9]
[59,3.0135254605054852E-9]
[60,1.2556356085439616E-9]
[61,5.1460475759998164E-10]
[62,2.0750191838708906E-10]
[63,8.2342031105987802E-11]
[64,3.2164855900776422E-11]
[65,{"$f":"_xlfn.POISSON.DIST(A169,$B$94,0)","v":1.2371098423375618E-11}]
[66,4.6860221300664561E-12]
[67,1.7485157201740515E-12]
[68,6.4283666182870063E-13]
[69,2.3291183399591017E-13]
[70,8.3182797855680996E-14]
[71,2.9289717554817128E-14]
[72,1.0170040817644819E-14]
[73,3.4828906909742688E-15]
[74,1.1766522604642794E-15]
["Total",{"$f":"SUM(B104:B178)","v":0.99999999999999911}]

{"sheet":"HYPGEOM.DIST","index":4,"n_rows":36,"n_cols":9,"rows_kept":36,"cut":false,"hidden":false,"merged":[]}
["Hypergeometric Distribution"]
["Similar to Binomial Distribution except: 1) the trails are not independent AND 2) the probability of success changes from trial to trial."]
["In Excel use: HYPGEOM.DIST(x,n,population_s,number_pop,cumulative)"]
["x = Number of Successes in Sample = Discrete Random Variable = sample_s"]
["n = Trials/Steps in Experiment = Sample Size = number_sample"]
["Number Successes in Pop. =  population_s"]
["Population Size = number_pop"]
["cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x"]
["OR"]
["cumulative = TRUE = 1 = probability mass function. Use to calculate <= x (everything from smallest up to and including x)"]
[]
["Probability of pulling 2 Face Cards  in 5 tries?"]
["Success = Face card",null,null,null,null,null,"Face Card (Not Ace)"]
["Event = pull 2 face cards (not an ace) in 5 tries"]
["x = Number of Successes in Sample = Discrete Random Variable = sample_s",null,null,null,null,null,2]
["n = Trials/Steps in Experiment = Sample Size = number_sample",null,null,null,null,null,5]
["Number Successes in Pop. =  population_s",null,null,null,null,null,12]
["Population Size = number_pop",null,null,null,null,null,52]
["cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x",null,null,null,null,null,0]
["Number of Sample Points",null,null,null,null,null,{"$f":"COMBIN(G16,G15)","v":10},null,{"$f":"_xlfn.FORMULATEXT(G20)","v":"=COMBIN(G16,G15)"}]
[]
[null,"Probability of pulling 2 Face Cards  in 5 tries"]
[null,"Probability of pulling 2 Face Cards  in 5 tries"]
[]
[]
["Sample Point","Step 1","Step 2","Step 3","Step 4","Step 5","Prob."]
["Sample Point 1","F","F","NF","NF","NF",{"$f":"12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48","v":2.5090036014405754E-2},null,{"$f":"_xlfn.FORMULATEXT(G27)","v":"=12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48"}]
["Sample Point 2","F","NF","F","NF","NF",{"$f":"12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48"]
["Sample Point 3","F","NF","NF","F","NF",{"$f":"12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48"]
["Sample Point 4","F","NF","NF","NF","F",{"$f":"12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48"]
["Sample Point 5","NF","F","F","NF","NF",{"$f":"(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48"]
["Sample Point 6","NF","F","NF","F","NF",{"$f":"(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48"]
["Sample Point 7","NF","F","NF","NF","F",{"$f":"(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48"]
["Sample Point 8","NF","NF","F","F","NF",{"$f":"(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48"]
["Sample Point 9","NF","NF","F","NF","F",{"$f":"(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48","v":2.5090036014405761E-2},null,"=(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48"]
["Sample Point 10","NF","NF","NF","F","F",{"$f":"(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48"]

{"sheet":"HYPGEOM.DIST (an)","index":5,"n_rows":35,"n_cols":9,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
["Hypergeometric Distribution"]
["Similar to Binomial Distribution except: 1) the trails are not independent AND 2) the probability of success changes from trial to trial."]
["In Excel use: HYPGEOM.DIST(x,n,population_s,number_pop,cumulative)"]
["x = Number of Successes in Sample = Discrete Random Variable = sample_s"]
["n = Trials/Steps in Experiment = Sample Size = number_sample"]
["Number Successes in Pop. =  population_s"]
["Population Size = number_pop"]
["cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x"]
["OR"]
["cumulative = TRUE = 1 = probability mass function. Use to calculate <= x (everything from smallest up to and including x)"]
[]
["Probability of pulling 2 Face Cards  in 5 tries?"]
["Success = Face card",null,null,null,null,null,"Face Card (Not Ace)"]
["Event = pull 2 face cards (not an ace) in 5 tries"]
["x = Number of Successes in Sample = Discrete Random Variable = sample_s",null,null,null,null,null,2]
["n = Trials/Steps in Experiment = Sample Size = number_sample",null,null,null,null,null,5]
["Number Successes in Pop. =  population_s",null,null,null,null,null,12]
["Population Size = number_pop",null,null,null,null,null,52]
["cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x",null,null,null,null,null,0]
["Number of Sample Points",null,null,null,null,null,{"$f":"COMBIN(G16,G15)","v":10},null,{"$f":"_xlfn.FORMULATEXT(G20)","v":"=COMBIN(G16,G15)"}]
[]
[null,"Probability of pulling 2 Face Cards  in 5 tries",null,null,null,null,{"$f":"SUM(G26:G35)","v":0.25090036014405764},null,{"$f":"_xlfn.FORMULATEXT(G22)","v":"=SUM(G26:G35)"}]
[null,"Probability of pulling 2 Face Cards  in 5 tries",null,null,null,null,{"$f":"_xlfn.HYPGEOM.DIST(G15,G16,G17,G18,0)","v":0.2509003601440577},null,{"$f":"_xlfn.FORMULATEXT(G23)","v":"=HYPGEOM.DIST(G15,G16,G17,G18,0)"}]
[]
["Sample Point","Step 1","Step 2","Step 3","Step 4","Step 5","Prob."]
["Sample Point 1","F","F","NF","NF","NF",{"$f":"12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48","v":2.5090036014405754E-2},null,{"$f":"_xlfn.FORMULATEXT(G26)","v":"=12/52*11/51*(50-10)/50*(49-10)/49*(48-10)/48"}]
["Sample Point 2","F","NF","F","NF","NF",{"$f":"12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*11/50*(49-10)/49*(48-10)/48"]
["Sample Point 3","F","NF","NF","F","NF",{"$f":"12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*11/49*(48-10)/48"]
["Sample Point 4","F","NF","NF","NF","F",{"$f":"12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=12/52*(51-11)/51*(50-11)/50*(49-11)/49*11/48"]
["Sample Point 5","NF","F","F","NF","NF",{"$f":"(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*11/50*(49-10)/49*(48-10)/48"]
["Sample Point 6","NF","F","NF","F","NF",{"$f":"(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*11/49*(48-10)/48"]
["Sample Point 7","NF","F","NF","NF","F",{"$f":"(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48","v":2.5090036014405768E-2},null,"=(52-12)/52*12/51*(50-11)/50*(49-11)/49*11/48"]
["Sample Point 8","NF","NF","F","F","NF",{"$f":"(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*12/50*11/49*(48-10)/48"]
["Sample Point 9","NF","NF","F","NF","F",{"$f":"(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48","v":2.5090036014405761E-2},null,"=(52-12)/52*(51-12)/51*12/50*(49-11)/49*11/48"]
["Sample Point 10","NF","NF","NF","F","F",{"$f":"(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48","v":2.5090036014405764E-2},null,"=(52-12)/52*(51-12)/51*(50-12)/50*12/49*11/48"]

{"sheet":"H(2)","index":6,"n_rows":37,"n_cols":7,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
["Example 2:"]
["Success = Face card",null,null,null,"Face Card (Not Ace)"]
["Event = pull 2 face cards (not an ace) in 5 tries"]
["x = Number of Successes in Sample = Discrete Random Variable = sample_s",null,null,null,2]
["n = Trials/Steps in Experiment = Sample Size = number_sample",null,null,null,5]
["Number Successes in Pop. =  population_s",null,null,null,12]
["Population Size = number_pop",null,null,null,52]
["cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x",null,null,null,0]
[]
["X = Pull Face in 5 tries","P(x)"]
[0]
[1]
[2]
[3]
[4]
[5]
["Total"]
[]
["Calculate the probability of getting 0 Face cards OR 1 face card OR 2 face cards in 5 tries:"]
["X","P(X)","SUM"]
[2,{"$f":"\"P(x<=\"&A21&\")\"","v":"P(x<=2)"}]
[null,null,"HYPGEOM.DIST"]
[]
[]
[]
["Example 3:"]
["During the financial crisis of 2008, of the ten biggest banks, only three increase lending after they were given TARP funds of about 2 Billion dolars were given out."]
[{"$f":"\"If you took at random sample of \"&B32&\" of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, all 3?\"","v":"If you took at random sample of 4 of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, all 3?"}]
[]
["Population size =",10]
["success in pop",3]
["Sample size",4]
["Success =","Did lend $"]
["x = Number","# that did lend in sample"]
["x","P(x)",null,null,null,null,"P(x)"]
[1,null,null,null,null,null,{"$f":"3/10*(9-2)/9*(8-2)/8*(7-2)/7*B32","v":0.5}]
[3]

{"sheet":"H(2an)","index":7,"n_rows":37,"n_cols":5,"rows_kept":37,"cut":false,"hidden":false,"merged":[]}
["Example 2:"]
["Success = Face card",null,null,null,"Face Card (Not Ace)"]
["Event = pull 2 face cards (not an ace) in 5 tries"]
["x = Number of Successes in Sample = Discrete Random Variable = sample_s",null,null,null,2]
["n = Trials/Steps in Experiment = Sample Size = number_sample",null,null,null,5]
["Number Successes in Pop. =  population_s",null,null,null,12]
["Population Size = number_pop",null,null,null,52]
["cumulative = FALSE = 0 = probability mass function. Use to calculate exactly x",null,null,null,0]
[]
["X = Pull Face in 5 tries","P(x)"]
[0,{"$f":"_xlfn.HYPGEOM.DIST(A11,$E$5,$E$6,$E$7,0)","v":0.25318127250900352}]
[1,{"$f":"_xlfn.HYPGEOM.DIST(A12,$E$5,$E$6,$E$7,0)","v":0.42196878751500583}]
[2,0.2509003601440577]
[3,6.6026410564225743E-2]
[4,7.6184319881798905E-3]
[5,3.047372795271953E-4]
["Total",{"$f":"SUM(B11:B16)","v":0.99999999999999989}]
[]
["Calculate the probability of getting 0 Face cards OR 1 face card OR 2 face cards in 5 tries:"]
["X","P(X)","SUM"]
[2,{"$f":"\"P(x<=\"&A21&\")\"","v":"P(x<=2)"},{"$f":"SUM(B11:B13)","v":0.92605042016806705}]
[null,null,"HYPGEOM.DIST"]
[null,null,{"$f":"_xlfn.HYPGEOM.DIST(A21,E5,E6,E7,1)","v":0.92605042016806716}]
[]
[]
["Example 3:"]
["During the financial crisis of 2008, of the ten biggest banks, only three increase lending after they were given TARP funds of about 2 Billion dolars were given out."]
[{"$f":"\"If you took at random sample of \"&B32&\" of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, all 3?\"","v":"If you took at random sample of 4 of the  ten biggest banks at that time, what is the probability that 1 of them would have increased lending, all 3?"}]
[]
["Population size =",10]
["success in pop",3]
["Sample size",4]
["Success =","Did lend $"]
["x = Number","# that did lend in sample"]
["x","P(x)",null,"P(x)"]
[1,{"$f":"_xlfn.HYPGEOM.DIST(A36,$B$32,$B$31,$B$30,0)","v":0.49999999999999994},null,{"$f":"3/10*(9-2)/9*(8-2)/8*(7-2)/7*B32","v":0.5}]
[3,{"$f":"_xlfn.HYPGEOM.DIST(A37,$B$32,$B$31,$B$30,0)","v":3.3333333333333291E-2}]