Review Test3 Stat Sum09

ReviewforTest3Statistics(Sections5.4,6.1,6.2,7.1,7.2,7.3,7.4,8.1,8.2, 9.1,9.2)Name___________________________________Youmayusethecardboardtables,providedthattherearenomarksonthesesheets.Onshortanswerproblemsunlesstoldotherwise,onlyusethecalculatorsstatisticalpackagetocheck.Note:= xP(X=x) =np

2x= (x-)2P(X=x) = x2P(X=x) -2 = np(1-p)

P(X=x)=nCxpx(1-p)n-x

x= x=n

p^=p p

^=p(1-p)

n

x-z/2ntox+z/2

n

E=z/2n

n z/2E

2

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

1) Astudywasrecentlydonethatemphasizedtheproblemweallfacewithdrinkinganddriving.FourhundredaccidentsthatoccurredonaSaturdaynightwereanalyzed.Twoitemsnotedwerethenumberofvehiclesinvolvedandwhetheralcoholplayedaroleintheaccident.Thenumbersareshownbelow:

NumberofVehiclesInvolvedDidAlcoholPlayaRole? 1 2 3ormore TotalsYes 58 93 19 170No 25 172 33 230Totals 83 265 52 400

Giventhatanaccidentinvolvedmultiplevehicles,whatwhatistheprobabilitythatitinvolvedalcohol?

1)

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

2) TheconditionalprobabilityofeventG,giventheknowledgethateventHhasoccurred,wouldbewrittenas_____.

A) P(G) B) P(G|H) C) P(H|G) D) P(H)

2)


Findtheconditionalprobability.3) InAnnescommunitycollege,40.6%ofstudentsareAsianand4.9%areAsianchemistry

majors.WhatpercentageofAsianstudentsarechemistrymajors?3)

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4) Anautoinsurancecompanywasinterestedininvestigatingaccidentratesfordriversindifferentagegroups.Thefollowingcontingencytablewasbasedonarandomsampleofdriversandprovidesajointprobabilitydistributionfordriversbyagegroupandaccidentrate.

0.137 0.182 0.370 0.689

0.068 0.086 0.101 0.255

0.027 0.015 0.013 0.055

Supposeoneofthesepeopleisselectedatrandom.Computetheprobabilitythatthepersonisagedover45giventhatinthepastthreeyearstheyhavehadnoaccidents.

4)


Solvetheproblem.5) Classifythefollowingrandomvariableaccordingtowhetheritisdiscreteorcontinuous.

ThenumberofcupsofcoffeesoldinacafeteriaduringlunchA) continuous B) discrete

5)

6) Classifythefollowingrandomvariableaccordingtowhetheritisdiscreteorcontinuous.ThetemperatureindegreesFahrenheitonJuly4thinJuneau,Alaska

A) continuous B) discrete

6)

7) AnApplePieCompanyknowsthatthenumberofpiessoldeachdayvariesfromdaytoday.Theownerbelievesthaton50%ofthedaysshesells100pies.Onanother25%ofthedaysshesells150pies,andshesells200piesontheremaining25%ofthedays.Tomakesureshehasenoughproduct,theownerbakes200pieseachdayatacostof$2.50each.Assumeanypiesthatgounsoldarethrownoutattheendoftheday.Ifshesellsthepiesfor$5each,findtheprobabilitydistributionforherdailyprofit.(Notethateverydayshespends$2.50foreachofthe200pies.)

A)Profit P(profit)$300 .5$550 .25$800 .25

B)Profit P(profit)$500 .5$750 .25$1000 .25

C)Profit P(profit)$0 .5$250 .25$500 .25

D)Profit P(profit)$250 .5$375 .25$500 .25

7)

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8) Therandomvariablexrepresentsthenumberofteststhatapatiententeringahospitalwillhavealongwiththecorrespondingprobabilities.Graphtheprobabilityhistogram.

x 0 1 2 3 4

P(x) 317

517

617

217

117

8)

9) Therandomvariablexrepresentsthenumberofcreditcardsthatadultshavealongwiththecorrespondingprobabilities.Findthemeanandstandarddeviationfortherandomvariablex.

x P(x)0 0.491 0.052 0.323 0.074 0.07

9)

10) Adicegameinvolvesthrowingthreediceandbettingononeofthesixnumbersthatareonthedice.Thegamecosts$6toplay,andyouwinifthenumberyoubetappearsonanyofthedice.Thedistributionfortheoutcomesofthegame(includingtheprofit)isshownbelow:

Numberofdicewithyournumber Profit ProbabilityofObserving0 -$6 125/2161 $6 75/2162 $8 15/2163 $18 1/216

Findyourexpectedprofitfromplayingthisgame.

10)

11) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Youspinanumberwheelthathas11numbers850times.Therandomvariablerepresentsthewinningnumbersoneachspinofthewheel.

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12) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Surveying250prisonerstoseewhethertheyareservingtimefortheirfirstoffense.Therandomvariablerepresentsthenumberofprisonersservingtimefortheirfirstoffense.

12)

13) Sixty-fivepercentofmenconsiderthemselvesknowledgeablefootballfans.If10menarerandomlyselected,findtheprobabilitythatexactlyfourofthemwillconsiderthemselvesknowledgeablefans.UsetheBinomialProbabilityDistributionFunction.Showwork.

13)

14) Assumethatmaleandfemalebirthsareequallylikelyandthatthebirthofanychilddoesnotaffecttheprobabilityofthegenderofanyotherchildren.Findtheprobabilityofatmostthreeboysintenbirths.

14)

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15) Atestconsistsof80multiplechoicequestions,eachwithfivepossibleanswers,onlyoneofwhichiscorrect.Findthemeanandthestandarddeviationofthenumberofcorrectanswers.

15)


16) Webelievethat83%ofthepopulationofallBusinessStatisticsIstudentsconsiderstatisticsanexcitingsubject.Supposewerandomlyandindependentlyselected39studentsfromthepopulation.Supposeweobservedfewerthanfiveinoursamplethatconsiderstatisticstobeanexcitingsubject.Makeaninferenceaboutthebeliefthat83%ofthestudentsconsiderstatisticstobeanexcitingsubject.(Findtheprobabilitythat0to4studentsfindStatisicsexcitingiftheprobablityis0.83thattheywill.)

A) Itisimpossibletomakeanyinferencesaboutthe83%numberbasedonthisinformation.B) The83%numberisexactlyright.C) The83%numberistoolow.Therealpercentageishigherthan83%.D) The83%numberistoohigh.Therealpercentageislowerthan83%.

16)

17) Thegraphofanormalcurveisgiven.Usethegraphtoidentifythevalueof and.

70 79 88 97 106 115 124A) =97,=9 B) =9, = 97 C) = 27, = 97 D) =97,=27

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18) Compareagraphofthenormaldensityfunctionwithmeanof0andstandarddeviationof1withagraphofanormaldensityfunctionwithmeanequalto4andstandarddeviationof1.Thegraphswould

A) Havethesameheightbutonewouldbeshifted4unitstotheright.B) Havenohorizontaldisplacementbutonewouldbesteeperthattheother.C) Havethesameheightbutonewouldbeshifter4unitstotheleft.D) Havenohorizontaldisplacementbutonewouldbeflatterthantheother.

18)

19) Compareagraphofthenormaldensityfunctionwithmeanof0andstandarddeviationof1withagraphofanormaldensityfunctionwithmeanequalto0andstandarddeviationof0.5.Thegraphswould

A) Havethesameheightbutonewouldbeshifter4unitstotheleft.B) Havenohorizontaldisplacementbutonewouldbesteeperthattheother.C) Havethesameheightbutonewouldbeshifted4unitstotheright.D) Haveahorizontaldisplacementandonewouldbeflatterthantheother.

19)

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20) ThehighestpointonthegraphofthenormaldensitycurveislocatedatA) + B) ItsmeanC) +3 D) Aninflectionpoint

20)


21) Theaveragempg(milespergallon)ofanewmodelofmotorcycleisknowntobenormallydistributedwithmean=27.4mpgandstandarddeviation=2.9mpg.(a)Drawanormalcurvewiththeparameterslabeled.(b)Shadetheregionthatrepresentstheproportionofmpgsbetween29.3and23.7.(c)SupposetheareaunderthenormalcurvetobetweenX=29.3andX=23.7is0.6419.Providetwointerpretationsofthisresult.

21)

ArandomvariableXisnormallydistributedwith = 60.ConvertthevalueofXtoaZ-score,ifthestandarddeviationisasgiven.

22) X=72;=8 22)


Fillintheblanksbystandardizingthenormallydistributedvariable.23) Davedrivestoworkeachmorningataboutthesametime.Hiscommutetimeisnormally

distributedwithameanof41minutesandastandarddeviationof4minutes.Thepercentageoftimethathiscommutetimeliesbetween33and37minutesisequaltotheareaunderthestandardnormalcurvebetween___and___.

A) 0,1 B) -2.5,-1.5 C) -2,-1 D) -1.5,-0.5

23)


Solvetheproblem.UseTableIVforquestions1- 9.Useacalculatoronlytocheck.24) Findtheareaunderthestandardnormalcurvetotheleftofz= 1.25. 24)

25) Findtheareaunderthestandardnormalcurvebetweenz= -1.5andz= 2.5. 25)

26) Forastandardnormalcurve,findthez-scorethatseparatesthebottom90%fromthetop10%.

26)

27) Findthez-scoresforwhich90%ofthedistributionsarealiesbetween-zandz. 27)

28) IQtestscoresarenormallydistributedwithameanof101 andastandarddeviationof20.AnindividualsIQscoreisfoundtobe111.Findthez-scorecorrespondingtothisvalue.

28)

Determinetheareaunderthestandardnormalcurvethatliesbetween:29) z=1andz=2 29)

Solvetheproblem.30) Aphysicalfitnessassociationisincludingthemileruninitssecondary-schoolfitnesstest.

Thetimeforthiseventforboysinsecondaryschoolisknowntopossessanormaldistributionwithameanof470secondsandastandarddeviationof40seconds.Findtheprobabilitythatarandomlyselectedboyinsecondaryschoolcanrunthemileinlessthan378seconds.

30)

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31) Thelengthoftimeittakescollegestudentstofindaparkingspotinthelibraryparkinglotfollowsanormaldistributionwithameanof7.0minutesandastandarddeviationof1minute.Findtheprobabilitythatarandomlyselectedcollegestudentwilltakebetween5.5and8.0minutestofindaparkingspotinthelibrarylot.

31)

32) Afirmbelievestheinternalrateofreturnforitsproposedinvestmentcanbestbedescribedbyanormaldistributionwithmean45%andstandarddeviation3%.Whatistheprobabilitythattheinternalrateofreturnfortheinvestmentwillbeatleast40.5%?

32)


33) Theamountofcornchipsdispensedintoa48-ouncebagbythedispensingmachinehasbeenidentifiedaspossessinganormaldistributionwithameanof48.5ouncesandastandarddeviationof0.2ounce.Whatchipamountrepresentsthe67thpercentileforthebagweightdistribution?

A) 48.63ounces B) 48.59ounces C) 48.09 ounces D) 48.13ounces

33)

Useanormalprobabilityplottoasseswhetherthesampledatacouldhavecomefromapopulationthatisnormallydistributed.

34) Thefollowingdatarepresentarandomsampleofthenumberofsharesofapharmaceuticalcompanysstocktradedfor20daysin2000.(Useacalculatortodrawthenormalprobabilityplot.)

4.41 9.33 10.83 7.95 14.275.72 10.12 9.37 12.53 13.684.67 8.97 12.02 7.18 27.978.14 10.57 4.71 7.67 11.31A) notnormallydistributed B) normallydistributed

34)

Solvetheproblem.35) Thenumberofviolentcrimescommittedinadaypossessesadistributionwithameanof 4.1

crimesperdayandastandarddeviationof6crimesperday.Arandomsampleof100dayswasobserved,andthesamplemeannumberofcrimesforthesamplewascalculated.Describethesamplingdistributionofthesamplemean.

A) shapeunknownwithmean=4.1andstandarddeviation= 0.6B) approximatelynormalwithmean= 4.1 andstandarddeviation= 6C) approximatelynormalwithmean= 4.1 andstandarddeviation= 0.6D) shapeunknownwithmean=4.1andstandarddeviation= 6

35)


Forsamplesofthespecifiedsizefromthepopulationdescribed,findthemeanandstandarddeviationofthesamplemeanx.

36) Themeanandthestandarddeviationofthesampledpopulationare,respectively,113.9and32.1.n=64(Roundtoonedecimalplace.)

36)

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Identifythedistributionofthesamplemean.Inparticular,statewhetherthedistributionof xisnormalorapproximatelynormalandgiveitsmeanandstandarddeviation.

37) Theweightsofpeopleinacertainpopulationarenormallydistributedwithameanof153lbandastandarddeviationof23lb.Determinethesamplingdistributionofthemeanforsamplesofsize5.

A) Approximatelynormal,mean=153 lb,standarddeviation= 10.29 lbB) Approximatelynormal,mean=153 lb,standarddeviation= 4.6 lbC) Normal,mean=153lb,standarddeviation= 10.29 lbD) Normal,mean=153lb,standarddeviation= 23 lb

37)


Solvetheproblem.38) Thelengthsofpregnanciesarenormallydistributedwithameanof264 daysanda

standarddeviationof20days.If64womenarerandomlyselected,findtheprobabilitythattheyhaveameanpregnancybetween264daysand266days.

38)


Findtheindicatedprobabilityorpercentageforthesamplingerror.39) Scoresonanaptitudetestarenormallydistributedwithameanof220andastandarddeviationof

10.Determinethepercentageofsamplesofsize25thathaveameanscorewithin3pointsofthepopulationmeanscoreof220.

A) 93.32% B) 38.30% C) 86.64% D) 13.36%

39)

Solvetheproblem.40) Assumethattheheightsofmenarenormallydistributedwithameanof68.2 inchesanda

standarddeviationof2.8inches.If64menarerandomlyselected,findtheprobabilitythattheyhaveameanheightgreaterthan69.2inches.

A) 0.8188 B) 9.9671 C) 0.0021 D) 0.9005

40)


41) Todeterminetheviewsonissuesthataffectthelivesoftheresidentsofavillage,thevillageselectmenrandomlychose800familiestoparticipateinasurveyoflifeattitudes.Thevillagereceived628completedsurveys.Whatisthesampleproportionofcompletedsurveys?

41)


42) Anationalcatererdeterminedthat87%ofthepeoplewhosampledtheirfoodsaidthatitwasdelicious.Ifthe144peopleattheValleyRidgeNursingHomearegiventhesamefood,andasked

bytableswhatthedeliciousnessofthefood,whatisthemeanofthesamplingdistributionof p^?

A) 0.87 B) 0.19 C) 1.25 D) 0.42

42)


43) Anationalcatererdeterminedthat37%ofthepeoplewhosampledtheirfoodsaidthatitwasdelicious.Ifthe144peopleattheValleyRidgeNursingHomearegiventhesamefood,andaskedbytableswhatthedeliciousnessofthefood,whatisthestandard

deviationofthesamplingdistributionofp^?

43)

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44) TheNationalAssociationofRealtorsestimatesthat23%ofallhomespurchasedin2004wereconsideredinvestmentproperties.Ifasampleof800homessoldin2004isobtainedwhatistheprobabilitythatatmost200homesaregoingtobeusedasinvestmentproperty?

44)


Findtherequestedvalue.45) Aresearcherwishestoestimatethemeanrestingheartrateforlong-distancerunners.Arandom

sampleof12long-distancerunnersyieldsthefollowingheartrates,inbeatsperminute.

71 62 65 60 69 7278 79 73 65 60 63

Usethedatatoobtainapointestimateofthemeanrestingheartrateforalllongdistancerunners.A) 66.4beatsperminute B) 64.8 beatsperminuteC) 68.1beatsperminute D) 69.8 beatsperminute

45)

46) Computethecriticalvaluez/2thatcorrespondstoa95%levelofconfidence.A) 1.96 B) 1.645 C) 2.33 D) 2.575

46)


Solvetheproblem.47) Inasampleof10randomlyselectedwomen,itwasfoundthattheirmeanheightwas63.4

inches.Frompreviousstudies,itisassumedthatthepopulationstandarddeviation, ,is2.4.Assumethattheheightofwomenisnormallydistributed.Constructthe95%confidenceintervalforthepopulationmean.

47)


48) Inarandomsampleof60computers,themeanrepaircostwas$150withapopulationstandarddeviationof$36.Constructa99%confidenceintervalforthepopulationmean.

A) ($537,$654) B) ($18,$54) C) ($238,$274) D) ($138,$162)

48)


Determinethemarginoferrorinestimatingthepopulationmean, .49) Asampleof44washingmachinesyieldsameanreplacementtimeof9.0 years.Assuming

that=2.3years,findthemarginoferrorinestimatingatthe90%levelofconfidence.49)

Determinethesamplesizeneededtoestimate forthegivensituation.50) E=4,=35,(1-)=.90 50)

Solvetheproblem.51) Inordertosetrates,aninsurancecompanyistryingtoestimatethenumberofsickdays

thatfulltimeworkersatanautorepairshoptakeperyear.Apreviousstudyindicatedthatthestandarddeviationwas2.1days.a)Howlargeasamplemustbeselectedifthecompanywantstobe90%confidentthatthetruemeandiffersfromthesamplemeanbynomorethan1day?b)Repeatpart(a)usinga95%confidenceinterval.Whichlevelofconfidencerequiresalargersamplesize?Explain.

51)

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Findthespecifiedt-value.52) Forat-curvewithdf=4,find t 0.05 .

A) 4.604 B) 2.132 C) 1.645 D) 2.35352)

Solvetheproblem.53) Findthecriticalt-valueusedforaconfidenceintervalwithaconfidencelevelof99%(c=0.99)

andn=10.A) 1.833 B) 2.262 C) 3.250 D) 2.2821

53)


54) Findthecriticalt-valuethatcorrespondstoc= 0.95andn= 16.(Note;confidencelevelwrittenasadecimal=c)

54)

Findtheconfidenceintervalspecified.Assumethatthepopulationisnormallydistributed.55) Asociologistdevelopsatesttomeasureattitudesaboutpublictransportation,and27

randomlyselectedsubjectsaregiventhetest.Assumethatthepopulationisnormallydistributed.Themeanscoreofthesampleis76.2andthesamplestandarddeviationis21.4.Constructthe95%confidenceintervalforthemeanscoreofallsuchsubjects.

55)

56) Constructa95%confidenceintervalforthepopulationmean,.Assumethepopulationhasanormaldistribution.Arandomsampleof16fluorescentlightbulbshasameanlifeof645hourswithastandarddeviationof31hours.

56)

57) a)Constructa95%confidenceintervalforthepopulationmean,.Assumethepopulationhasanormaldistribution.Inarandomsampleof26computers,themeanrepaircostwas$157withastandarddeviationof$33.b)Supposeyoudidsomeresearchonrepaircostsforcomputersandfoundthatthestandarddeviationis=33.Usethenormaldistributiontoconstructa95%confidenceintervalforthepopulationmean,.Comparetheresults.

57)

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AnswerKeyTestname:REVIEWFORTEST3STATSUM09

1) 112317

2) B3) 12.1%4) 0.5375) B6) A7) C8)

9) mean:1.18;standarddeviation:1.3010) -$0.7511) Notabinomialexperiment.Therearemorethantwooutcomes.12) binomialexperiment.13) 0.06914) 0.17215) mean:16;standarddeviation:3.5777087616) D17) A18) A19) B20) B

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21) (a),(b)

(c)Thetwointerpretationsare:(1)theproportionofmpgbetween29.3and23.7is0.6419and(2)theprobabilitythatarandomlyselectedmpgisbetween29.3and23.7is0.6419.

22) 1.523) C24) 0.894425) 0.927026) 1.2827) (-1.645,1.645)28) 0.5029) 14%30) .010731) .774532) Letxbetheinternalrateofreturn.Thenxisanormalrandomvariablewith = 45%and=3%.Todeterminethe

probabilitythatxisatleast40.5%,weneedtofindthez-valueforx=40.5%.

z=x-

=40.5-45

3=-1.5

P(x40.5%)=1-P(z-1.5)=1-0.0668=.933233) B34) A35) C36)

x=113.9;

x=4.0

37) C38) 0.288139) C40) C41) 0.78542) A43) 0.0444) 0.909945) C46) A47) (61.9,64.9)48) D49) 0.57years

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50) 208(Recall:Alwaysroundupforn.)51) a)12

b)17;A95%confidenceintervalrequiresalargersamplethana90%confidenceintervalbecausemoreinformationisneededfromthepopulationtobe95%confident.

52) B53) C54) 2.13155) 67.7to84.756) (628.5,661.5)57) a)($143.67,$170.33)

b)($144.32,$169.68);Thet-confidenceintervaliswider.

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Review Test3 Stat Sum09