{"text_format":"1","workbook":"xlsx","n_sheets":7,"sheets":["Tax fraud","Defective parts","Dirt","Complaints","Coin flips","Baseball","Breakdowns"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":0,"defined_names":19,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Tax fraud","index":0,"n_rows":20,"n_cols":3,"rows_kept":20,"cut":false,"hidden":false,"merged":[[0,1,0,8]]}
[null,"Tax fraud"]
[]
[null,"The IRS catches about 25% of all fraudulent returns each year.  (This is far"]
[null,"higher than the truth, but makes for simpler calculations.)  (a) What is the"]
[null,"probability that you could get away with fraud 5 years in a row?  (b) What is the"]
[null,"expected number of fraudulent returns you could file before being caught for"]
[null,"the first time?  (c) If you cheat every year, how likely is it that you'll be caught"]
[null,"twice in 5 years (assuming that the IRS does not increase its scrutiny of you after"]
[null,"the first detected offense)?"]
[]
[]
[null,0.25,"Pr( fraudulent return is caught )"]
[null,5,"n ( years )"]
[]
[null,{"$f":"(1-Pr_fraud)^n","v":0.2373046875},"Pr( not caught n years in a row )"]
[null,{"$f":"(1/Pr_fraud)-1","v":3},"E[ number of years prior to being caught first time )"]
[]
[null,2,"k ( times caught )"]
[null,{"$f":"BINOMDIST(k,n,Pr_fraud,FALSE)","v":0.26367187499999994},"Pr( caught k times in n years )"]
[null,{"$f":"COMBIN(n,k)*Pr_fraud^k*(1-Pr_fraud)^(n-k)","v":0.263671875},"same, explicitly"]

{"sheet":"Defective parts","index":1,"n_rows":23,"n_cols":13,"rows_kept":23,"cut":false,"hidden":false,"merged":[[0,1,0,9],[12,1,22,1]]}
[null,"Defective parts"]
[]
[null,"When a new machine is functioning properly, only 3% of the items produced are"]
[null,"defective. Assume that we will randomly select two parts produced on the"]
[null,"machine and that we are interested in the number of defective parts found."]
[null,"Compute the probabilities associated with finding no defects, exactly one defect,"]
[null,"and two defects."]
[]
[]
[null,null,null,0.03,"defect rate"]
[null,null,null,"sample size"]
[null,null,null,1,2,3,4,5,6,7,8,9,10]
[null,"defectives",0,{"$f":"BINOMDIST($C13,D$12,$D$10,FALSE)","v":0.97},0.94089999999999996,0.91267299999999996,0.88529281000000004,0.85873402570000001,0.83297200492900003,0.80798284478113003,0.78374335943769613,0.76023105865456519,0.73742412689492831]
[null,null,1,{"$f":"BINOMDIST($C14,D$12,$D$10,FALSE)","v":2.9999999999999995E-2},5.8199999999999988E-2,8.468100000000002E-2,0.10952075999999999,0.13279392150000002,0.15457212462600001,0.17492412103509,0.19391588274747118,0.21161070704817797,0.22806931759636956]
[null,null,2,{"$error":"#NUM!"},8.9999999999999976E-4,2.6190000000000007E-3,5.0808599999999987E-3,8.2140570000000038E-3,1.1951452935000006E-2,1.6230073085730004E-2,2.0990894524210813E-2,2.6178644170908608E-2,3.1741606057226729E-2]
[null,null,3,{"$error":"#NUM!"},{"$error":"#NUM!"},2.7000000000000013E-5,1.047600000000002E-4,2.5404300000000007E-4,4.928434199999997E-4,8.3660170545000068E-4,1.2984058468583988E-3,1.8891805071789734E-3,2.6178644170908624E-3]
[null,null,4,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},8.0999999999999966E-7,3.928499999999993E-6,1.1431934999999997E-5,2.5874279550000007E-5,5.0196102326999967E-5,8.7642394662942137E-5,1.416885380384229E-4]
[null,null,5,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},2.4299999999999963E-8,1.414259999999998E-7,4.8014127000000081E-7,1.2419654183999999E-6,2.7105895256580027E-6,5.2585436797765254E-6]
[null,null,6,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},7.2900000000000079E-10,4.9499100000000041E-9,1.9205650800000024E-8,5.58884438280001E-8,1.3552947628290009E-7]
[null,null,7,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},2.1870000000000001E-11,1.6971120000000046E-10,7.4078938800000007E-10,2.3952190212000038E-9]
[null,null,8,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},6.560999999999994E-13,5.7277530000000123E-12,2.7779602049999878E-11]
[null,null,9,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},1.968299999999996E-14,1.909251000000001E-13]
[null,null,10,{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},{"$error":"#NUM!"},5.9048999999999828E-16]

{"sheet":"Dirt","index":2,"n_rows":22,"n_cols":3,"rows_kept":22,"cut":false,"hidden":false,"merged":[[0,1,0,8]]}
[null,"Removing dirt and stains"]
[]
[null,"A new clothes-washing compound is found to remove excess dirt and stains"]
[null,"satisfactorily on 88% of the items washed. Assume that 10 items are to be"]
[null,"washed with the new compound."]
[]
[null,"What is the probability of satisfactory results on all 10 items?"]
[]
[null,"What is the probability of at least two items being found with unsatisfactory"]
[null,"results?"]
[]
[]
[null,0.88,"Pr( success on a single item )"]
[]
[null,10,"n (number of items washed)"]
[null,{"$f":"Pr_success^washed","v":0.2785009760094021},"Pr( success on all n items )"]
[]
[null,2,"d (at least these many items still dirty)"]
[]
[null,null,"Pr( failure on at least d items )"]
[null,{"$f":"BINOMDIST(washed-dirty,washed,Pr_success,TRUE)","v":0.34172496579595862},"= Pr( n-d or fewer cleaned successfully )"]
[null,{"$f":"1-BINOMDIST(dirty-1,washed,1-Pr_success,TRUE)","v":0.34172496579595868},"= 1 - Pr( d-1 or fewer still dirty )"]

{"sheet":"Complaints","index":3,"n_rows":49,"n_cols":5,"rows_kept":49,"cut":false,"hidden":false,"merged":[[0,1,0,8],[27,3,27,4]]}
[null,"Looking at a sample: The binomial distribution"]
[]
[null,"The greatest number of complaints by owners of two-year-old automobiles pertain to"]
[null,"electrical system performance (Consumer Reports 1995 Buyer’s Guide). Assume that"]
[null,"an annual questionnaire sent to owners of over 300 makes and models of"]
[null,"automobiles reveeals that 10% of the owners of two-year-old automobiles found"]
[null,"trouble spots in the electrical system that included the starter, alternator, battery,"]
[null,"switch controls, instruments, wiring, lights, and radio."]
[]
[null,"What is the probability that a sample of 12 owners of two-year-old automobiles will"]
[null,"find exactly two owners with electrical system problems?"]
[]
[null,"What is the probability that a sample of 12 owners of two-year-old automobiles will"]
[null,"find at least two owners with electrical system problems?"]
[]
[null,"What is the probability that a sample of 20 owners of two-year-old automobiles will"]
[null,"find at least one owner with electrical system problems?"]
[]
[]
[null,0.1,"Pr( electrical problem )"]
[]
[null,12,"sample size"," ¬ change these to 20 and 1 to solve part c."]
[null,2,"k"]
[]
[null,{"$f":"BINOMDIST(kk,sample,Pr_problem,FALSE)","v":0.230127770466},"Pr( exactly k in sample experience problems )"]
[null,{"$f":"1-BINOMDIST(kk-1,sample,Pr_problem,TRUE)","v":0.34099774821100004},"Pr( at least k in sample experience problems )"]
[]
[null,null,"k","Pr( exactly k in sample\nexperience problems )"]
[null,null,0,{"$f":"COMBIN(sample,C29)*Pr_problem^C29*(1-Pr_problem)^(sample-C29)","v":0.28242953648100017},{"$f":"BINOMDIST(C29,sample,Pr_problem,FALSE)","v":0.282429536481}]
[null,null,1,{"$f":"COMBIN(sample,C30)*Pr_problem^C30*(1-Pr_problem)^(sample-C30)","v":0.37657271530800024},{"$f":"BINOMDIST(C30,sample,Pr_problem,FALSE)","v":0.37657271530800002}]
[null,null,2,0.23012777046600016,0.230127770466]
[null,null,3,8.5232507580000061E-2,8.5232507580000019E-2]
[null,null,4,2.1308126895000019E-2,2.1308126895000012E-2]
[null,null,5,3.7881114480000037E-3,3.7881114480000024E-3]
[null,null,6,4.9105148400000029E-4,4.910514840000005E-4]
[null,null,7,4.6766808000000043E-5,4.6766808000000043E-5]
[null,null,8,3.2476950000000033E-6,3.2476950000000054E-6]
[null,null,9,1.6038000000000017E-7,1.6038000000000046E-7]
[null,null,10,5.3460000000000061E-9,5.3459999999999822E-9]
[null,null,11,1.0800000000000012E-10,1.0799999999999989E-10]
[null,null,12,1.0000000000000014E-12,1.000000000000001E-12]
[null,null,13,{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,null,14,{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,null,15,{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,null,16,{"$error":"#NUM!"},{"$error":"#NUM!"}]
[null,null,17,{"$f":"COMBIN(sample,C46)*Pr_problem^C46*(1-Pr_problem)^(sample-C46)","v":{"$error":"#NUM!"}},{"$error":"#NUM!"}]
[null,null,18,{"$f":"COMBIN(sample,C47)*Pr_problem^C47*(1-Pr_problem)^(sample-C47)","v":{"$error":"#NUM!"}},{"$error":"#NUM!"}]
[null,null,19,{"$f":"COMBIN(sample,C48)*Pr_problem^C48*(1-Pr_problem)^(sample-C48)","v":{"$error":"#NUM!"}},{"$error":"#NUM!"}]
[null,null,20,{"$f":"COMBIN(sample,C49)*Pr_problem^C49*(1-Pr_problem)^(sample-C49)","v":{"$error":"#NUM!"}},{"$error":"#NUM!"}]

{"sheet":"Coin flips","index":4,"n_rows":27,"n_cols":11,"rows_kept":27,"cut":false,"hidden":false,"merged":[[0,1,0,8]]}
[null,"Coin flipping"]
[]
[null,"What is the expected number of coin flips needed in order to get"]
[null,"at least one head and at least one tail?"]
[]
[null,null,null,null,null,null,null,{"$f":"MIN(H7:H27)","v":4},null,{"$f":"ADDRESS(ROW($H$6),COLUMN($H$6))","v":"$H$6"},"monitored cell"]
[null,"The first table to the right simulates",null,null,null,1,{"$f":"IF(RAND()<=0.5,\"H\",\"T\")","v":"H"},null,null,3.0015499999999999,"mean"]
[null,"a sequence of 20 coin flips, and",null,null,null,2,{"$f":"IF(RAND()<=0.5,\"H\",\"T\")","v":"H"},{"$f":"IF(G8<>G7,F8,\"\")","v":""},null,1.4118808489300065,"sample standard deviation"]
[null,"at the top of the third column",null,null,null,3,"H",{"$f":"IF(G9<>G8,F9,\"\")","v":""},null,2,"minimum"]
[null,"determines the number of flips",null,null,null,4,"T",4,null,18,"maximum"]
[null,"needed to get both a head and",null,null,null,5,"T","",null,100000,"number of simulation runs"]
[null,"a tail.",null,null,null,6,"T",""]
[null,null,null,null,null,7,"H",7,null,{"$f":"1.96*J8/SQRT(J11)","v":8.7509281640862149E-3},"margin of error (95% confidence)"]
[null,"Press \"F9\" a few times to see that",null,null,null,8,"T",8]
[null,"the average hovers around 3.",null,null,null,9,"H",9]
[null,null,null,null,null,10,"H",""]
[null,{"$f":"1+1/0.5","v":3},"answer",null,null,11,"H","",null,"Notice that we did, at least once, get one outcome"]
[null,null,null,null,null,12,"T",12,null,"17 times in a row before the other occurred"]
[null,"(Of course, the simulation",null,null,null,13,"T",""]
[null,"calculations will be a bit",null,null,null,14,"T",""]
[null,"off if there are 20 consecutive",null,null,null,15,"T",""]
[null,"heads or tails. This should",null,null,null,16,"H",16]
[null,"only happen about one time",null,null,null,17,"H",""]
[null,"in 500,000.)",null,null,null,18,"T",18]
[null,null,null,null,null,19,"H",19]
[null,null,null,null,null,20,"T",20]
[null,null,null,null,null,null,null,21]

{"sheet":"Baseball","index":5,"n_rows":24,"n_cols":3,"rows_kept":24,"cut":false,"hidden":false,"merged":[[0,1,0,8]]}
[null,"Baseball"]
[]
[null,"Assume that a baseball pitcher has a 60% chance of throwing a strike when"]
[null,"he pitches his knuckleball, and that the outcomes of separate knuckleball"]
[null,"pitches are independent of one another. Further assume that he’s facing a"]
[null,"batter who can’t hit his knuckleball at all. What is the chance that the pitcher"]
[null,"will strike the batter out (i.e., throw three strikes before he throws four"]
[null,"non-strikes (balls))?"]
[]
[]
[null,0.6,"Pr(any particular pitch is a strike)"]
[]
[null,{"$f":"strike^3","v":0.216},"Pr(3 strikes)"]
[null,{"$f":"BINOMDIST(2,3,strike,FALSE)*strike","v":0.25919999999999999},"Pr(1 ball and 2 strikes, then a strike)"]
[null,{"$f":"BINOMDIST(2,4,strike,FALSE)*strike","v":0.20736000000000002},"Pr(2 balls and 2 strikes, then a strike)"]
[null,{"$f":"BINOMDIST(2,5,strike,FALSE)*strike","v":0.13824},"Pr(3 balls and 2 strikes, then a strike)"]
[]
[null,{"$f":"SUM(B13:B16)","v":0.82079999999999997},"total"]
[]
[null,{"$f":"BINOMDIST(3,6,1-strike,TRUE)","v":0.82079999999999997},"quicker"]
[]
[null,"(The \"quicker\" approach is based on the observation that every sequence of six"]
[null,"pitches includes either at least three strikes or at least four balls (and that only"]
[null,"one of these two cases can occur.)"]

{"sheet":"Breakdowns","index":6,"n_rows":53,"n_cols":3,"rows_kept":53,"cut":false,"hidden":false,"merged":[[0,1,0,8],[34,1,34,8]]}
[null,"Breakdowns"]
[]
[null,"A new automated production process has had an average of 1.5 breakdowns per"]
[null,"day. Because of the cost associated with a breakdown, management is concerned"]
[null,"about the possibility of having three or more breakdowns per day. Assume that"]
[null,"breakdowns occur randomly, that the probability of a breakdown is the same for"]
[null,"any two time intervals of equal length, and that breakdowns in one period are"]
[null,"independent of breakdowns in other periods. What is the probability of having"]
[null,"three or fewer breakdowns in the course of one day?"]
[]
[]
[null,"This problem can be done directly using the Poisson distribution,"]
[null,"or approximately using the binomial distribution (and breaking the day"]
[null,"into a number of \"periods\")."]
[]
[null,1.5,"mean number of breakdowns per day"]
[null,3,"k (number of breakdowns in a day)"]
[]
[null,{"$f":"POISSON(breaks,break_rate,TRUE)","v":0.93435754562154982},"Pr( k  or fewer breakdowns in a day )"]
[null,"=POISSON(breaks,break_rate,TRUE)"]
[]
[null,{"$f":"24*60","v":1440},"periods in a day (minutes)"]
[null,{"$f":"break_rate/periods","v":1.0416666666666667E-3},"breakdown rate per minute"]
[null,{"$f":"BINOMDIST(breaks,periods,B23,TRUE)","v":0.93445567041683542},"approximate answer, using binomial distribution"]
[null,"=BINOMDIST(breaks,periods,B23,TRUE)"]
[]
[null,"The reason the binomial-distribution approach is approximate, rather than exact, is that"]
[null,"it doesn't allow for the possibility of two or more breakdowns during the same period. If the"]
[null,"periods are very short, this doesn't differ much from reality, i.e., the breakdown rate per"]
[null,"period is close to the probability of a single breakdown in a period."]
[]
[]
[null,"Here's another example:"]
[]
[null,"Typographical errors"]
[]
[null,"An experienced typist makes approximately 1 mistake every 3 pages. What is the"]
[null,"probability that he makes at most two mistakes while typing a 10-page paper?"]
[]
[]
[null,3,"pages / error"]
[null,{"$f":"1/pages_per_error","v":0.33333333333333331},"errors / page (I.e., error rate )"]
[null,10,"pages"]
[null,2,"k (errors)"]
[]
[null,{"$f":"POISSON(errors,error_rate*pages,TRUE)","v":0.35277615643394045},"Pr( k or fewer errors in n pages )"]
[]
[null,"Using the binomial distribution as an approximation:"]
[]
[null,1500,"characters/page, roughly"]
[null,{"$f":"error_rate/B50","v":2.2222222222222221E-4},"Pr(a particular character is in error)"]
[]
[null,{"$f":"BINOMDIST(errors,chars_per_page*pages,B51,TRUE)","v":0.3527467918053207},"Pr( k or fewer errors in n pages )"]