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attached are the questions and the excel file needed for question 3.all questions are to be answered in excel

Model MPG Cylinders Engine Disp Horsepower Weight Accelerate Year Origin amc ambassador dpl 15.0 8 390 190 3850 8.5 70 American amc gremlin 21.0 6 199 90 2648 15.0 70 American amc hornet 18.0 6 199 97 2774 15.5 70 American amc rebel sst 16.0 8 304 150 3433 12.0 70 American buick estate wagon (sw) 14.0 8 455 225 3086 10.0 70 American buick skylark 320 15.0 8 350 165 3693 11.5 70 American chevrolet chevelle malibu 18.0 8 307 130 3504 12.0 70 American chevrolet impala 14.0 8 454 220 4354 9.0 70 American chevrolet monte carlo 15.0 8 400 150 3761 9.5 70 American chevy c20 10.0 8 307 200 4376 15.0 70 American dodge challenger se 15.0 8 383 170 3563 10.0 70 American dodge d200 11.0 8 318 210 4382 13.5 70 American ford f250 10.0 8 360 215 4615 14.0 70 American ford galaxie 500 15.0 8 429 198 4341 10.0 70 American ford maverick 21.0 6 200 85 2587 16.0 70 American ford torino 17.0 8 302 140 3449 10.5 70 American hi 1200d 9.0 8 304 193 4732 18.5 70 American plymouth 'cuda 340 14.0 8 340 160 3609 8.0 70 American plymouth duster 22.0 6 198 95 2833 15.5 70 American plymouth fury iii 14.0 8 440 215 4312 8.5 70 American plymouth satellite 18.0 8 318 150 3436 11.0 70 American pontiac catalina 14.0 8 455 225 4425 10.0 70 American audi 100 ls 24.0 4 107 90 2430 14.5 70 European bmw 2002 26.0 4 121 113 2234 12.5 70 European peugeot 504 25.0 4 110 87 2672 17.5 70 European saab 99e 25.0 4 104 95 2375 17.5 70 European volkswagen 1131 deluxe sedan 26.0 4 97 46 1835 20.5 70 European datsun pl510 27.0 4 97 88 2130 14.5 70 Japanese toyota corona mark ii 24.0 4 113 95 2372 15.0 70 Japanese amc gremlin 19.0 6 232 100 2634 13.0 71 American amc hornet sportabout (sw) 18.0 6 258 110 2962 13.5 71 American amc matador 18.0 6 232 100 3288 15.5 71 American chevrolet chevelle malibu 17.0 6 250 100 3329 15.5 71 American chevrolet impala 14.0 8 350 165 4209 12.0 71 American chevrolet vega (sw) 22.0 4 140 72 2408 19.0 71 American chevrolet vega 2300 28.0 4 140 90 2264 15.5 71 American dodge monaco (sw) 12.0 8 383 180 4955 11.5 71 American ford country squire (sw) 13.0 8 400 170 4746 12.0 71 American ford galaxie 500 14.0 8 351 153 4154 13.5 71 American ford mustang 18.0 6 250 88 3139 14.5 71 American ford torino 500 19.0 6 250 88 3302 15.5 71 American mercury capri 2000 23.0 4 122 86 2220 14.0 71 American plymouth cricket 26.0 4 91 70 1955 20.5 71 American plymouth fury iii 14.0 8 318 150 4096 13.0 71 American plymouth satellite custom 16.0 6 225 105 3439 15.5 71 American pontiac catalina brougham 14.0 8 400 175 4464 11.5 71 American pontiac firebird 19.0 6 250 100 3282 15.0 71 American pontiac safari (sw) 13.0 8 400 175 5140 12.0 71 American fiat 124b 30.0 4 88 76 2065 14.5 71 European opel 1900 28.0 4 116 90 2123 14.0 71 European peugeot 304 30.0 4 79 70 2074 19.5 71 European volkswagen model 111 27.0 4 97 60 1834 19.0 71 European datsun 1200 35.0 4 72 69 1613 18.0 71 Japanese datsun pl510 27.0 4 97 88 2130 14.5 71 Japanese toyota corolla 1200 31.0 4 71 65 1773 19.0 71 Japanese toyota corona 25.0 4 113 95 2228 14.0 71 Japanese amc ambassador sst 17.0 8 304 150 3672 11.5 72 American amc matador (sw) 15.0 8 304 150 3892 12.5 72 American buick lesabre custom 13.0 8 350 155 4502 13.5 72 American chevrolet chevelle concours (sw) 13.0 8 307 130 4098 14.0 72 American chevrolet impala 13.0 8 350 165 4274 12.0 72 American chevrolet vega 20.0 4 140 90 2408 19.5 72 American chrysler newport royal 13.0 8 400 190 4422 12.5 72 American dodge colt (sw) 28.0 4 98 80 2164 15.0 72 American dodge colt hardtop 25.0 4 97.5 80 2126 17.0 72 American ford galaxie 500 14.0 8 351 153 4129 13.0 72 American ford gran torino (sw) 13.0 8 302 140 4294 16.0 72 American ford pinto (sw) 22.0 4 122 86 2395 16.0 72 American ford pinto runabout 21.0 4 122 86 2226 16.5 72 American mercury marquis 11.0 8 429 208 4633 11.0 72 American oldsmobile delta 88 royale 12.0 8 350 160 4456 13.5 72 American plymouth fury iii 15.0 8 318 150 4135 13.5 72 American plymouth satellite custom (sw) 14.0 8 318 150 4077 14.0 72 American pontiac catalina 14.0 8 400 175 4385 12.0 72 American peugeot 504 (sw) 21.0 4 120 87 2979 19.5 72 European renault 12 (sw) 26.0 4 96 69 2189 18.0 72 European volkswagen 411 (sw) 22.0 4 121 76 2511 18.0 72 European volkswagen type 3 23.0 4 97 54 2254 23.5 72 European volvo 145e (sw) 18.0 4 121 112 2933 14.5 72 European datsun 510 (sw) 28.0 4 97 92 2288 17.0 72 Japanese mazda rx2 coupe 19.0 3 70 97 2330 13.5 72 Japanese toyota corolla 1600 (sw) 27.0 4 97 88 2100 16.5 72 Japanese toyota corona hardtop 24.0 4 113 95 2278 15.5 72 Japanese toyouta corona mark ii (sw) 23.0 4 120 97 2506 14.5 72 Japanese amc ambassador brougham 13.0 8 360 175 3821 11.0 73 American amc gremlin 18.0 6 232 100 2789 15.0 73 American amc hornet 18.0 6 232 100 2945 16.0 73 American amc matador 14.0 8 304 150 3672 11.5 73 American buick century 350 13.0 8 350 175 4100 13.0 73 American buick electra 225 custom 12.0 8 455 225 4951 11.0 73 American chevrolet caprice classic 13.0 8 400 150 4464 12.0 73 American chevrolet impala 11.0 8 400 150 4997 14.0 73 American chevrolet malibu 13.0 8 350 145 3988 13.0 73 American chevrolet monte carlo s 15.0 8 350 145 4082 13.0 73 American chevrolet nova custom 16.0 6 250 100 3278 18.0 73 American
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chevrolet vega 21.0 4 140 72 2401 19.5 73 American chrysler new yorker brougham 13.0 8 440 215 4735 11.0 73 American dodge coronet custom 15.0 8 318 150 3777 12.5 73 American dodge dart custom 15.0 8 318 150 3399 11.0 73 American ford country 12.0 8 400 167 4906 12.5 73 American ford gran torino 14.0 8 302 137 4042 14.5 73 American ford ltd 13.0 8 351 158 4363 13.0 73 American ford maverick 18.0 6 250 88 3021 16.5 73 American ford pinto 19.0 4 122 85 2310 18.5 73 American mercury capri v6 21.0 6 155 107 2472 14.0 73 American mercury marquis brougham 12.0 8 429 198 4952 11.5 73 American oldsmobile omega 11.0 8 350 180 3664 11.0 73 American oldsmobile vista cruiser 12.0 8 350 180 4499 12.5 73 American plymouth custom suburb 13.0 8 360 170 4654 13.0 73 American plymouth duster 23.0 6 198 95 2904 16.0 73 American plymouth fury gran sedan 14.0 8 318 150 4237 14.5 73 American plymouth valiant 18.0 6 225 105 3121 16.5 73 American pontiac grand prix 16.0 8 400 230 4278 9.5 73 American audi 100ls 20.0 4 114 91 2582 14.0 73 European fiat 124 sport coupe 26.0 4 98 90 2265 15.5 73 European fiat 128 29.0 4 68 49 1867 19.5 73 European opel manta 24.0 4 116 75 2158 15.5 73 European saab 99le 24.0 4 121 110 2660 14.0 73 European volkswagen super beetle 26.0 4 97 46 1950 21.0 73 European volvo 144ea 19.0 4 121 112 2868 15.5 73 European datsun 610 22.0 4 108 94 2379 16.5 73 Japanese maxda rx3 18.0 3 70 90 2124 13.5 73 Japanese toyota carina 20.0 4 97 88 2279 19.0 73 Japanese toyota mark ii 20.0 6 156 122 2807 13.5 73 Japanese amc hornet 19.0 6 232 100 2901 16.0 74 American amc matador 16.0 6 258 110 3632 18.0 74 American amc matador (sw) 14.0 8 304 150 4257 15.5 74 American buick century luxus (sw) 13.0 8 350 150 4699 14.5 74 American chevrolet chevelle malibu classic 16.0 6 250 100 3781 17.0 74 American chevrolet nova 15.0 6 250 100 3336 17.0 74 American chevrolet vega 25.0 4 140 75 2542 17.0 74 American dodge colt 28.0 4 90 75 2125 14.5 74 American dodge coronet custom (sw) 14.0 8 318 150 4457 13.5 74 American ford gran torino 16.0 8 302 140 4141 14.0 74 American ford gran torino (sw) 14.0 8 302 140 4638 16.0 74 American ford pinto 26.0 4 122 80 2451 16.5 74 American plymouth duster 20.0 6 198 95 3102 16.5 74 American plymouth satellite sebring 18.0 6 225 105 3613 16.5 74 American audi fox 29.0 4 98 83 2219 16.5 74 European fiat 124 tc 26.0 4 116 75 2246 14.0 74 European fiat 128 24.0 4 90 75 2108 15.5 74 European fiat x1.9 31.0 4 79 67 2000 16.0 74 European opel manta 26.0 4 97 78 2300 14.5 74 European volkswagen dasher 26.0 4 79 67 1963 15.5 74 European datsun 710 32.0 4 83 61 2003 19.0 74 Japanese datsun b210 31.0 4 79 67 1950 19.0 74 Japanese honda civic 24.0 4 120 97 2489 15.0 74 Japanese subaru 26.0 4 108 93 2391 15.5 74 Japanese toyota corolla 1200 32.0 4 71 65 1836 21.0 74 Japanese toyota corona 31.0 4 76 52 1649 16.5 74 Japanese amc gremlin 20.0 6 232 100 2914 16.0 75 American amc matador 15.0 6 258 110 3730 19.0 75 American amc pacer 19.0 6 232 90 3211 17.0 75 American buick century 17.0 6 231 110 3907 21.0 75 American buick skyhawk 21.0 6 231 110 3039 15.0 75 American chevroelt chevelle malibu 16.0 6 250 105 3897 18.5 75 American chevrolet bel air 15.0 8 350 145 4440 14.0 75 American chevrolet monza 2+2 20.0 8 262 110 3221 13.5 75 American chevrolet nova 18.0 6 250 105 3459 16.0 75 American ford ltd 14.0 8 351 148 4657 13.5 75 American ford maverick 15.0 6 250 72 3158 19.5 75 American ford mustang ii 13.0 8 302 129 3169 12.0 75 American ford pinto 23.0 4 140 83 2639 17.0 75 American ford pinto 18.0 6 171 97 2984 14.5 75 American mercury monarch 15.0 6 250 72 3432 21.0 75 American plymouth fury 18.0 6 225 95 3785 19.0 75 American plymouth grand fury 16.0 8 318 150 4498 14.5 75 American plymouth valiant custom 19.0 6 225 95 3264 16.0 75 American pontiac astro 23.0 4 140 78 2592 18.5 75 American pontiac catalina 16.0 8 400 170 4668 11.5 75 American audi 100ls 23.0 4 115 95 2694 15.0 75 European peugeot 504 23.0 4 120 88 2957 17.0 75 European saab 99le 25.0 4 121 115 2671 13.5 75 European volkswagen dasher 25.0 4 90 71 2223 16.5 75 European volkswagen rabbit 29.0 4 90 70 1937 14.0 75 European volvo 244dl 22.0 4 121 98 2945 14.5 75 European datsun 710 24.0 4 119 97 2545 17.0 75 Japanese honda civic cvcc 33.0 4 91 53 1795 17.5 75 Japanese toyota corolla 29.0 4 97 75 2171 16.0 75 Japanese toyota corona 24.0 4 134 96 2702 13.5 75 Japanese amc hornet 22.5 6 232 90 3085 17.6 76 American amc matador 15.5 8 304 120 3962 13.9 76 American amc pacer d/l 17.5 6 258 95 3193 17.8 76 American cadillac seville 16.5 8 350 180 4380 12.1 76 American capri ii 25.0 4 140 92 2572 14.9 76 American chevrolet chevelle malibu classic 17.5 8 305 140 4215 13.0 76 American chevrolet chevette 29.0 4 85 52 2035 22.2 76 American chevrolet nova 22.0 6 250 105 3353 14.5 76 American chevrolet woody 24.5 4 98 60 2164 22.1 76 American chevy c10 13.0 8 350 145 4055 12.0 76 American dodge aspen se 20.0 6 225 100 3651 17.7 76 American
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1. (17Points)Irecentlyhadtoreplacebothfrontheadlightso',tycar.Theiifeexpectancy of my headlights f"u;;; "xporrerrtial ai.Liu,rtlon i,itt u MTBF of 1500 hours' That is' the expected.romb". of hours until ruilrr"'i. iloo no.r.r" For the purposes of this problem assume that both rr""irigilr, *.r"1*tiary installed at the same time' are identical models and are alwaYs on at the same trme' a"Whatistheprobabilitythattherightheadlightwillburnouting50hoursorlessof oPeration? b.Whatistheprobabilitythatbothheadlightsburnouting50hoursorlessofoperation? c. Sure enough the right headlight bums out at the 950th hour of operation' Now suppose that I get the ,igfr, fr."aiight repliced. er iu- atiting.some time liter, I nervously await the rightheadlightfailingafterg50hoursbutnothinghappens"fstartfeelingluckyand believe that the right headlight will r^t ui ftutt uiotfi 950 hours' What is the probability that my right headlight will last for ai least 1900 hours given that it has not failed after 950 hours? (20 Points) use Excel to illustrate the central Limit Theorem when sampling from a binomial distribution" a. Generate at least 1000 random samples (you can generate more if you wish), each with 4 observations, from a binomial random ";r*bil;;here p:0.2 (theprobability of a success)' and n:10 trials. That is, the random "".i;1; t."p. .r"ri, the. number of successes in 10 trials' where the probability of a success is o.z. calc"laie the sample mean for each sample' rPlotafrequencyhistogramofthesamplemeansandcommentontheplot. rDeterminetherange,-.u,u,,dstandarddeviationofthel000samplemeans' rHowdothecalculatedmeanandstandarddeviationcompalewithwhatyou *o,1J have expected from a theoretical analysis? b. Generate at least 1000 random samples (you can generate 1io^re if You wish)' each with 30 observations, from a binomial random #iuur" yith"" p:0'2 (the.probability o{ a success)' and n:10 triais. That is, the random ,"J"Ui. y ..pr.r.ni, the. number of successes in 10 trials' where the probability of a success is O.i- Catc,rlaie the sample mean for each sample' o Plot a liequency histogram of the sample means and comment on the p1ot" r Determine the range, -.u., urri standard deviation of the 1000 sample means' rHowdothecalculatedmeanandstandarddeviationcomparewithwhatyou would have expected from a theoretical analysis? 3.(13Points)TheCARS.XLSfilethatcamewithyourBerk&Careytextbookcontalns information on392 "armodels. Oata in the frleLcludes the miles per gallon (MPG) of each car, as well as the acceleration' weight and horsepower' a"Createtwoscattetplots,thefirstbetweenMPGandaccelerationandthesecondbetween weight and horsepower' Describe the relationships you see" 2.
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4. b" Find the standard deviation and coefficient of variation for MPG, acceleration, weight and horsepower, respectively' Intelpret tf" "'it'' p"Vl"g particular attention to the units of each measure. c.Findthecorrelationandcovariancebetweenacar,sMPGanditsacceleration"Interpretthe results, paying particular attention to the units of each measure' d. Find the correlation and covariance between a car,s MPG and its weight. Interpret the results, ,"r*t particular attention to the units of each measure ' e. Find the corelation and covariance between a car's MPG and its horsepower" Interpret the results, paying particular attention to the units of each measure' (18 Points) A certain market has both an expless checkout line and a super-express checkout line. Let Y denote the number of customers in line at the express checkout at a particular time of day, ]f,j i"ti Jenote the number of customers in line at the super- express checkout at the same time. Supp". . ,r,. joint probability mass function of Y and X is as given in the accompanying table' a. b. d. f. X p(x,y) 0 1 2 3 0 0.08 0.07 0.04 0 1 0.06 0.15 0.05 0.04 2 0.05 0.04 0.1 0.06 3 0 0.03 0.04 0.07 4 0 0.01 0.05 0.06 Whatistheprobabilitythatthenumberofcustomersinlineattheexpresscheckoutis3? Are X and Y independent random variables? Whatistheprobabilitythatthereisexactlyonecustomerineachlineatthesametime? what is the probability that the number of customers in the two lines are identical? You are interested in examining whether the express checko^r't haadles more customers than the super-expr"r, "tr."t o.ri. CJ. ..ut" tt e p.oUititity mass function of the random variable A' where A:Y-X. what is the probability that the express checkout has more customers than the super-express checkout, that is, the P(A > 0)'
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5. (17 points) An airport limousine can accommodate up to four passengers on any one trip' The company *1r u". .pt ;;;ri*"- of six reservations for a trip and a passenger must have a reservation. er"l" pt."i"us records, 2}oh of allthose making reservations do not appealforthetrip.Answerthefollowingquestions,assumingindependencewhenever appropriate. a. If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip? b. Suppose that the probability mass function of the number of reservations made is given in the accompanying table. Let i denote the number of passengers on a randomly selected trip' Obtain the probability mass function of X' (15 points) consider the clearance, c, between a shaft and a bearing" The shafts are mass produced such that the outside diameters, S, are normally and independently distributed withmeanp.=l.05inches,andastandarddeviationo,.Thebearingsareproducedsuch that the inside diameters, g, ure normally and independently distributed with mean trru : 1.06 inches and a standard deviation ou : 0.001 inch. If production of shafts is to be controiled so that no more than lo/oof randomly mated shafts and bearings will exhibit interference, what is the maximum allowable value of o'? Note that C: B - S" 6" Number of reservations
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