StatisticsforBusinessSpring2012.pdf

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1、Statisticsfor BusinessSpring2012Exam1Thursday,Feb.23100 pointsEXAM INSTRUCTIONS1.BubbleSheet:(a)Write and bubble yourName(last name,?rst name)(b)Write and bubble your8-digit Student ID Number(Begin in the leftmost box.)2.ExamBooklet:Write the informationbelow.NameStudent ID NumberTAs NameDiscussion

2、TimeSection Number3.ExamLocationsLocationSectionsTAsW128 CBA2A3AlanW290 CBA4A10Paul,Shih-Ming,Danlu,PatrickC20 PCA11A17Yinan,Congrui,Joseph,Silver100 PHA18A20,SCA,SCBKevin,Long,SeanLR2 VANSCC,SCDCristinaa4.Please sit with space between yourself and other students.5.You may use a calculator(but no ce

3、ll phone or dictionary),pencil,and one 81211sheetof paper,front and back,of handwrittenor word-processed notes.6.There are 44 questionsand one tableon 19 pages.Check your exam for these.7.The exam format is multiplechoice.Circle the singlebestansweron the exam bookletand?ll the corresponding bubble

4、on the bubble sheet with a No.2 pencil.Carefullyeraseany answers on the bubble sheet which you wish to change.8.You have two hours to complete the exam.9.When?nished,placethebubblesheetinsidethe?rstpageof theexambooklet.Depositbubblesheet andexambooklettogetherintoyourDiscussionfolder.10.The base sc

5、ore for the exam is 12 points.In addition,2 points are earned for each questionwhichis answered correctlyon the bubble sheet.Check ICON to see your score and alist of exam questions which were answered incorrectly.11.Youmay beginthe exam.1Questions14.In government data,a household consists of all oc

6、cupants of a dwelling unit,while a familyconsists of two or more persons who live together and are related by blood or marriage.Hereare the distributionsof household size and familysize in the UnitedStates:Numberof Persons1234567Householdprobability0.250.320.170.150.070.030.01Familyprobability0.000.

7、420.230.210.090.030.02Here are histograms:3HUVRQV3HUFHQW+RXVHKROG6LH3HUVRQV3HUFHQW)DPLO6LH(Answerquestionson nextpage)21.What is the mean familysize?(a)1.00(b)2.00(c)2.60(d)3.14(e)None of the answers is correctto the second decimal place2.What is the mean household size?(a)1.00(b)2.00(c)2.60(d)3.14(

8、e)None of the answers is correctto the second decimal place3.Which has the smallest standard deviation,household size or family size?(Hint:It is not necessary to perform any calculations to answer this question.It mayhelp to compare histograms.)(a)Household size(b)Family size(c)Neither,since the sta

9、ndard deviations are equal.4.Suppose thatthere are 9700 families in the Iowa Cityarea.Abouthow many of thefamilies would you expect to have between 3 and 6 persons?(a)2134(b)2910(c)3783(d)5432(e)None of the answers is correct to the nearest person3Questions510.Nguyen plays a game called Two Quarters

10、 and One Die with his friend.Each time the game is played,Nguyen pays the friend$5.In return,the friend pays Nguyen$x,where x is the random variablex=(number of heads from two quarters)+(face value from one die)after two fair quartersand one fair die are each tossed once.(Each quarterfalls either“he

11、ads”or“tails”and the die shows one of the face values“1”,“2”,“3”,“4”,“5”,“6.”)Hints:(1)Is the result of the die toss independent of the two quarter tosses?(2)It may help to write down the sample space.(Answerquestionson nextpage)45.Find P(x=1)(a)0.0417(b)0.1000(c)0.1667(d)0.6667(e)None of the answer

12、s is correctto the fourth decimal place6.Find P(x=8)(a)0.0417(b)0.1000(c)0.1667(d)0.4167(e)None of the answers is correctto the fourth decimal place7.Find P(x=2)(a)0.0417(b)0.1000(c)0.1250(d)0.4167(e)None of the answers is correctto the fourth decimal place8.What is the probabilitythat Nguyen makes

13、money(i.e.,that x exceeds 5)in any game?(a)0.0000(b)0.2500(c)0.5000(d)0.6667(e)None of the answers is correctto the fourth decimal place9.Find x=the average or expected value of x.(a)4(b)4.5(c)5(d)5.5(e)610.Is Nguyen smart to play many,many games with his friend over a long period of time?In other w

14、ords,does Nguyen make money by playing the game,on average?(a)Yes since Nguyen pays one dollar more than he receives,on average.(b)No since Nguyen pays one dollar more than he receives,on average.(c)Yes since Nguyen receives one dollar more than he pays,on average.(d)No since Nguyen receives one dol

15、lar more than he pays,on average.(e)None of the answers is correct.5Questions1112.A real estate agent has four master keys which can unlock the doors of hundreds of foreclosedhomes in Sacramento,California.Each master key can unlock the doors of multiplehomesbut only one master key can unlock the do

16、ors of any particularhome.The four keys appearto be identical.11.If the agent randomlyselects two of the four keys,whats the probabilitythatone ofthe selected keys will unlock the doors of the particularhome at 1234 MulberryLane?(a)0.063(b)0.167(c)0.250(d)0.333(e)0.50012.If the agent repeats this sa

17、me practice independentlyfor 10 di?erent homes,whatsthe probabilitythat she will be able to unlock the doors of?ve of the homes?(a)0.031(b)0.058(c)0.246(d)0.500(e)0.6236Questions1317.Microchipsproduced by Honeywell,Inc.at its plant in Phoenix,Arizonaare designed foruse in computers.Each manufactured

18、chip is subjected to four independent diagnostic tests:circuitry,consistency,speed and structuralintegrity.?A chip must pass all four tests to be classi?ed as acceptable and sold to computermanufacturers.?If the chip fails any of the tests it is classi?ed as defective and recycled rather than sold.T

19、he failure rates(probabilitiesof not passing)for the four tests are shown below:CircuitryConsistencySpeedStructuralIntegrityFailureRate0.010.030.020.01(Carryall calculationsto at leastsix decimalplaces.)(Answerquestionson nextpage)713.What percentage of chips are classi?ed as acceptable?(a)6.83(b)7.

20、00(c)93.00(d)93.17(e)None of the answers is correctto the second decimal place14.What percentage of chips are classi?ed as defective?(a)6.83(b)7.00(c)93.00(d)93.17(e)None of the answers is correctto the second decimal place15.What percentage of chips fail the test for circuitry,but pass the other th

21、ree tests?(a)0.00(b)0.94(c)13.78(d)14.29(e)None of the answers is correctto the second decimal place16.Whatpercentage of defective chips fail the test for circuitry,but pass the other threetests?(a)0.00(b)0.94(c)13.78(d)14.29(e)None of the answers is correctto the second decimal place17.What percent

22、age of acceptable chips fail the test for circuitry,but pass the other threetests?(a)0.00(b)0.94(c)86.22(d)85.71(e)None of the answers is correctto the second decimal place8Questions1820.A store manager observes how much timeeach of 100 shoppers spends in the store,inminutes.Some MINITAB outputis sh

23、own below.0LQXWHV)UHTXHQFDescriptiveStatistics:Time inStoreVariableNN*MeanSE MeanStDevMinimumQ1MedianQ3Time inStore100035.50.7587.517.91530.29634.80441.293VariableMaximumTime inStore56.93718.Approximatelywhat percentage of all customers spend between 28 and 35.5 minutesat the supermarket?(a)0.0(b)34

24、.0(c)47.5(d)81.5(e)None of the answers is correctto the?rst decimal place19.Approximatelywhat percentage of all customers spend between 20.5 and 43 minutesat the supermarket?(a)0.0(b)34.0(c)47.5(d)81.5(e)None of the answers is correctto the?rst decimal place20.Approximatelywhat percentage of all cus

25、tomers spend more than 12 minutes at thesupermarket?(a)0.0(b)34.0(c)47.5(d)81.5(e)None of the answers is correctto the?rst decimal place9Questions2123.A marketingconsultantobserves how much money each of 40 consecutive shoppers spendsat a supermarket,in dollars.The data are shown below.5.328.889.261

26、0.8112.6915.2315.6217.0017.3518.4319.5019.5420.5922.2223.0424.4725.1326.2426.2627.6528.0828.3832.0334.9837.3738.6439.1641.0242.9744.6745.4046.6949.3952.7554.8059.0760.2284.3685.7794.3821.Findthe best estimateof the minimumamountspent(in dollars)by the 90%ofcustomers who spend the most.(a)8.88(b)12.6

27、9(c)59.07(d)None of the answers is correct to the second decimal place(e)The answer cannot be determined withoutfurtherinformation22.Find the best estimate of the amount of money(in dollars)typically spent by customers.(Hint:Recall a similarquestion for fast-foodrestaurantmanagers in Santa Barbarafr

28、om the Topic 2 Notes.)(a)27.65(b)28.08(c)29.43(d)34.13(e)None of the answers is correct to the second decimal place23.Does it appear that at least 90%of all customers spend between$9.00 and$90.00?(a)Yes(b)No10Questions2434.A lie detector is an electronic device which useswires attached to a person s

29、skin to measurevarious physiologicalreadings.On the basis of those readings,the detector will indicate thatthe person being tested is either truthfulor deceptive(not being truthful.)Two lie detectors,A and B,operate independentlyof each other:?Lie DetectorA has probability0.9 of indicatingthata dece

30、ptive person is,indeed,deceptive.?Lie DetectorB has probability0.8 of indicatingthata deceptive person is,indeed,deceptive.24.If bothDetectorA and DetectorB are appliedto a deceptive person,whats theprobabilitythat neither detector indicates that the person is deceptive?(a)0.02(b)0.26(c)0.28(d)0.30(

31、e)None of the answers is correctto the second decimal place25.If bothDetectorA and DetectorB are appliedto a deceptive person,whats theprobabilitythatone detectorindicatesthatthe person is deceptive and the otherindicates that the person is truthful?(a)0.02(b)0.26(c)0.28(d)0.30(e)None of the answers

32、 is correctto the second decimal place(continued)11For the next four questions de?ne the random variablex=number of lie detectors which indicate deceptivewhen both DetectorA and Detector B are applied to a deceptive person.(Do not round any calculations.)26.Find x(a)0.25(b)0.50(c)1.70(d)3.47(e)None

33、of the answers is correctto the second decimal place27.Find x(a)0.25(b)0.50(c)1.70(d)3.47(e)None of the answers is correctto the second decimal place28.Find P(x x+x)(a)0.00(b)0.02(c)0.10(d)0.28(e)None of the answers is correctto the second decimal place29.Does x?t the de?nitionof a binomialrandom va

34、riable?(a)Yes(b)No since the probabilityof“success”changes from 0.9 for DetectorA to 0.8 forDetector B(c)No since x does not count the“numberof successes.”(continued)12For the next?ve questions suppose that Detector A(only)is applied to 20 persons.30.Find the probabilitythat Detector A indicates tha

35、t 18 or fewer are deceptive,if all 20are deceptive.(a)0.090(b)0.608(c)0.850(d)0.900(e)0.95731.Find the probabilitythat DetectorA indicates that more than 15 are deceptive,if all20 are deceptive.(a)0.043(b)0.250(c)0.608(d)0.750(e)0.95732.Find the probabilitythatDetector A indicates that exactly 16 ar

36、e deceptive,if all 20are deceptive.(a)0.090(b)0.133(c)0.608(d)0.800(e)0.95733.Find the probabilitythat Detector A indicates that fewer than 10 are deceptive,if all20 are deceptive.(a)0.000(b)0.100(c)0.450(d)0.500(e)1.00034.If Detector A indicates that 9 people are deceptive,what conclusion is warran

37、ted?(a)Exactlyone of the 20 persons is being truthful.(b)Exactlyone of the 20 persons is deceptive.(c)All 20 persons are truthful.(d)All 20 persons are deceptive.(e)None of the conclusions is warranted.13Questions3538.The American AutomobileAssociation(AAA)is a nationalorganizationwhich also has 50s

38、tate chapters.Members of the Iowa chapter of the AAAwould like to compare prices ofregular gasoline to prices of diesel fuel withinthe state of Iowa.In particular,suppose that the Iowa chapter would like to test the theory that diesel is moreexpensive on average than regular gasoline at Iowa service

39、 stations which sell both fuels,onSept.30,2011.The AAAnationalorganizationhas providedthe Iowa chapter witha database of prices,shown in the table below.The database was developed as follows:?Five zip codes were randomlyselected from all zip codes in the state of Minnesota,and?ve zip codes were rand

40、omly selected from all zip codes in the state of Iowa.?In each selected zip code,a service station which sells both fuels was randomlychosenfrom all such service stations in that zip code.The prices for both diesel and regulargas on Sept.30,2011 at the chosen stationwere recorded in the database.Pri

41、ce(dollars/gallon)Price(dollars/gallon)ZipCodeCityStateforRegularGasfor DieselFuel50005MinervaIowa3.663.7350021AnkenyIowa3.633.6055005BethelMinnesota3.813.8856258MarshallMinnesota3.863.9250101GaltIowa3.723.8056678BecidaMinnesota3.833.8855732PikeMinnesota3.933.9850438MillerIowa3.603.6752050GreeleyIow

42、a3.583.6455383NorwoodMinnesota3.843.8735.Perform Step 2 of the Inference Process.(a)All service stations in Iowa which serve both diesel and regular gas(b)All automobileusers in the state of Iowa(c)There are two populations:?Pop 1=All service stations in Iowa which serve both diesel and regular gas?

43、Pop 2=All service stations in Minnesota which serve both diesel and regulargas(d)There are two populations:?Pop 1=All automobileusers in the state of Iowa?Pop 2=All automobileusers in the state of Minnesota(e)There are two populations:?Pop 1=All zip codes in the state of Iowa?Pop 2=All zip codes in

44、the state of Minnesota(continued)1436.Perform Step 3 of the Inference Process.(a)Five service stations in Iowa whose prices for diesel and regular gas are recordedin the database(b)Five automobileusers in the state of Iowa who purchased fuel on Sept.30,2011(c)There are two samples:?Sample 1=Five ser

45、vice stations in Iowa whose prices for diesel and regulargas are recorded in the database?Sample 2=Five service stations in Minnesotawhose prices for diesel andregular gas are recorded in the database(d)There are two samples:?Sample 1=Five automobileusers in the state of Iowa who purchased fuel onSe

46、pt.30,2011?Sample 2=Five automobileusers in the state of Minnesota who purchasedfuel on Sept.30,2011(e)There are two samples:?Sample 1=Five zip codes in the state of Iowa from which a single servicestation is chosen?Sample 2=Five zip codes in the state of Minnesotafrom which a singleservice station

47、is chosen37.Perform Step 4 of the Inference Process.(a)?All cities in Iowa?All cities in Minnesota(b)?sample average price of diesel,in dollars?sample average price of regular gas,in dollars(c)?All zip codes in Iowa?All service stations in Iowa(d)?price of diesel,in dollars?price of regular gas,in d

48、ollars(e)?populationaverage price of diesel,in dollars?populationaverage price of regular gas,in dollars38.Does the theory appear to be correct?(a)Yes,since 3.797 3.746(b)No,since 3.797 3.746(c)Yes,since 3.688 3.638(d)No,since 3.688 3.638(e)More informationis needed before the theory can be evaluate

49、d15Questions3942.Short Answer.39.Provide the de?nitionof a statisticalpopulation(a)the precise set of units which are actually measured(b)a numerical characteristicof the parameter(c)the inference which generalizes from the sample summary to Step 3 in the Infer-ence Process(d)the subset of the sampl

50、e of interest(e)None of the answers is correct40.True or False:The sample is smaller than the populationin all statisticalapplications(a)True(b)False41.True or False:Greek letters such as and always represent populationparameters.(a)True(b)False42.True or False:The symbol x represents a sample stati