Ch.6 DiscreteProbabilityDistributions
6.1 DiscreteRandomVariables
1 Distinguishbetweendiscreteandcontinuousrandomvariables.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Classifythefollowingrandomvariableaccordingtowhetheritisdiscreteorcontinuous.
1) thenumberofbottlesofjuicesoldinacafeteriaduringlunch
A) discrete B) continuous
2) theheightsofthebookcasesinaschoollibrary
A) continuous B) discrete
3) thecostofaroadatlas
A) discrete B) continuous
4) thepressureofwatercomingoutofafirehose
A) continuous B) discrete
5) thetemperatureindegreesCelsiusonJanuary1stinFargo,NorthDakota
A) continuous B) discrete
6) thenumberofgoalsscoredinahockeygame
A) discrete B) continuous
7) thespeedofacaronaNewYorktollwayduringrushhourtraffic
A) continuous B) discrete
8) thenumberofemailsreceivedonanygivenday
A) discrete B) continuous
9) theageoftheoldestdoginakennel
A) continuous B) discrete
10) thenumberofpillsinanaspirinbottle
A) discrete B) continuous
Provideanappropriateresponse.
11) Thepeakshoppingtimeathomeimprovementstoreisbetween8:00am–11:00amonSaturdaymornings.
Managementatthehomeimprovementstorerandomlyselected35customerslastSaturdaymorningand
decidedtoobservetheirshoppinghabits.Theyrecordedthenumberofitemsthateachofthecustomers
purchasedaswellasthetotaltimethecustomersspentinthestore.Identifythetypesofvariablesrecordedby
thehomeimprovementstore.
A) numberofitems–discrete;totaltime–continuous
B) numberofitems–continuous;totaltime–continuous
C) numberofitems–continuous;totaltime–discrete
D) numberofitems–discrete;totaltime–discrete
12) Thenumberofviolentcrimescommittedinadaypossessesadistributionwithameanof1.8crimesperday
andastandarddeviationoffourcrimesperday.Arandomsampleof80dayswasobserved,andthesample
meannumberofcrimesforthesamplewascalculated.Thedatathatwascollectedinthisexperimentcouldbe
measuredwitha__________randomvariable.
A) discrete B) continuous
Page188
13) Arandomvariableis
A) anumericalmeasureoftheoutcomeofaprobabilityexperiment.
B) generatedbyarandomnumbertable.
C) thevariableforwhichanalgebraicequationissolved.
D) aqualitativeattributeofapopulation.
2 Identifydiscreteprobabilitydistributions.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Giventhetableofprobabilitiesfortherandomvariablex,doesthisformaprobabilitydistribution?Answer
YesorNo.
x5 10 15 20
P(x) 0.10 –0.30 0.50 0.70
A) No B) Yes
2) Giventhetableofprobabilitiesfortherandomvariablex,doesthisformaprobabilitydistribution?Answer
YesorNo.
x01234
P(x) 0.02 0.07 0.22 0.27 0.42
A) Yes B) No
3) Considerthediscreteprobabilitydistributiontotherightwhenansweringthefollowingquestion.Findthe
probabilitythatxequals5.
x2568
P(x) 0.16 ? 0.3 0.21
A) 0.33 B) 0.67 C) 1.65 D) 3.35
4) Considerthediscreteprobabilitydistributiontotherightwhenansweringthefollowingquestion.Findthe
probabilitythatxexceeds4.
x2468
P(x) 0.03 ? 0.08 0.31
A) 0.39 B) 0.97 C) 0.61 D) 0.58
5) AnApplePieCompanyknowsthatthenumberofpiessoldeachdayvariesfromdaytoday.Theowner
believesthaton50%ofthedaysshesells100pies.Onanother25%ofthedaysshesells150pies,andshesells
200piesontheremaining25%ofthedays.Tomakesureshehasenoughproduct,theownerbakes200pies
eachdayatacostof$2each.Assumeanypiesthatgounsoldarethrownoutattheendoftheday.Ifshesells
thepiesfor$4each,findtheprobabilitydistributionforherdailyprofit.
A)
Profit P(profit)
$0 0.5
$200 0.25
$400 0.25
B)
Profit P(profit)
$400 0.5
$600 0.25
$800 0.25
C)
Profit P(profit)
$200 0.5
$400 0.25
$600 0.25
D)
Profit P(profit)
$200 0.5
$300 0.25
$400 0.25
6) Thesumoftheprobabilitiesofadiscreteprobabilitydistributionmustbe
A) equaltoone. B)
b
etweenzeroandone.
C) greaterthanone. D) lessthanorequaltozero.
Page189
3 Constructprobabilityhistograms.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Therandomvariablexrepresentsthenumberofboysinafamilyofthreechildren.Assumingthatboysand
girlsareequallylikely,(a)constructaprobabilitydistribution,and(b)graphtheprobabilityhistogram.
2) Therandomvariablexrepresentsthenumberofteststhatapetenteringananimalshelterwillhavealongwith
thecorrespondingprobabilities.Graphtheprobabilityhistogram.
xP(x)
03
17
15
17
26
17
32
17
41
17
3) Therandomvariablexrepresentsthenumberofcreditcardsthatstudentshavealongwiththecorresponding
probabilities.Graphtheprobabilityhistogram.
x P(x)
0 0.49
1 0.05
2 0.32
3 0.07
40.07
4) InanItaliancafe,thefollowingprobabilitydistributionwasobtained.Therandomvariablexrepresentsthe
numberoftoppingsforalargepizza.Graphtheprobabilityhistogram.
x P(x)
0 0.30
1 0.40
2 0.20
3 0.06
40.04
5) Usethefrequencydistributionto(a)constructaprobabilitydistributionfortherandomvariablexwhich
representsthenumberofcarsperfamilyinatownof1000families,and(b)graphtheprobabilityhistogram.
Cars Families
0 125
1 428
2 256
3 108
483
Page190
4 Computeandinterpretthemeanofadiscreterandomvariable.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Calculatethemeanforthediscreteprobabilitydistributionshownhere.
x36712
P(x) 0.03 0.2 0.32 0.45
A) 8.93 B) 7 C) 28 D) 2.2325
2) Alabordersashipmentof100ratsaweek,52weeksayear,fromaratsupplierforexperimentsthatthelab
conducts.Pricesforeachweeklyshipmentofratsfollowthedistributionbelow:
Price $10.00 $12.50 $15.00
Probability 0.25 0.3 0.45
Supposethemeancostoftheratsturnedouttobe$13.00perweek.Interpretthisvalue.
A) Theaveragecostforallweeklyratpurchasesis$13.00.
B) Mostoftheweeksresultedinratcostsof$13.00.
C) Themediancostforthedistributionofratcostsis$13.00.
D) Theratcostthatoccursmoreoftenthananyotheris$13.00.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
3) Calculatethemeanforthediscreteprobabilitydistributionshownhere.
x2689
P(x) 0.2 0.3 0.3 0.2
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
4) Abaseballplayerisaskedtoswingatpitchesinsetsoffour.Theplayerswingsat100setsof4pitches.The
probabilitydistributionformakingaparticularnumberofhitsisgivenbelow.Determinethemeanforthis
discreteprobabilitydistribution.
x01234
P(x) 0.02 0.07 0.22 0.27 0.42
A) 3 B) 4 C) 2 D) 3.5
5) Theproducemanageratafarmerʹsmarketwasinterestedindetermininghowmanyorangesapersonbuys
whentheybuyoranges.Heaskedthecashiersoveraweekendtocounthowmanyorangesapersonbought
whentheyboughtorangesandrecordthisnumberforanalysisatalatertime.Thedataisgivenbelowinthe
table.TherandomvariablexrepresentsthenumberoforangespurchasedandP(x)representstheprobability
thatacustomerwillbuyxapples.Determinethemeannumberoforangespurchasedbyacustomer.
x12345678910
P(x) 0.05 0.19 0.20 0.25 0.12 0.10 0 0.08 0 0.01
A) 3.97 B) 5.50 C) 3 D) 4
Page191
6) Arandomnumbergeneratorissettogeneratesingledigitsbetween0and9.Onehundredandfiftyrandom
numbersaregenerated.Theprobabilitydistributionforthisrandomnumbergeneratorisgivenbelow.What
isthemeanofthisdistribution?
x0123456789
P(x) 0.09 0.12 0.11 0.08 0.09 0.13 0.10 0.07 0.10 0.11
A) 4.5 B) 6.6 C) 5 D) 7
7) Aseedcompanyhasatestplotinwhichitistestingthegerminationofahybridseed.Theyplant50rowsof40
seedsperrow.Afteratwo–weekperiod,theresearcherscounthowmanyseedperrowhavesprouted.They
notedthatleastnumberofseedstogerminatewas33andsomerowshadall40germinate.Thegermination
dataisgivenbelowinthetable.Therandomvariablexrepresentsthenumberofseedinarowthat
germinatedandP(x)representstheprobabilityofselectingarowwiththatnumberofseedgerminating.
Determinethemeannumberofseedsperrowthatgerminated.
x33 34 35 36 37 38 39 40
P(x) 0.02 0.06 0.10 0.20 0.24 0.26 0.10 0.02
A) 36.9 B) 36.5 C) 36 D) 0.13
8) Amanageraskedheremployeeshowmanytimestheyhadgivenbloodinthelastyear.Theresultsofthe
surveyaregivenbelow.TherandomvariablexrepresentsthenumberoftimesapersongavebloodandP(x)
representstheprobabilityofselectinganemployeewhohadgivenbloodthatpercentofthetime.Whatisthe
meannumberoftimesapersongavebloodbasedonthissurvey?
x0123456
P(x) 0.30 0.25 0.20 0.12 0.07 0.04 0.02
A) 1.6 B) 3.0 C) 2.0 D) 0.14
5 Interpretthemeanofadiscreterandomvariableasanexpectedvalue.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Alabordersashipmentof100ratsaweek,52weeksayear,fromaratsupplierforexperimentsthatthelab
conducts.Pricesforeachweeklyshipmentofratsfollowthedistributionbelow:
Price $10.00 $12.50 $15.00
Probability 0.2 0.3 0.5
Howmuchshouldthelabbudgetfornextyearʹsratordersassumingthisdistributiondoesnotchange.(Hint:
findtheexpectedprice.)
A) $689.00 B) $13.25 C) $1325.00 D) $3,582,800.00
2) MammaTemtebakessixpiesadaythatcost$2eachtoproduce.On15%ofthedaysshesellsonlytwopies.On
30%ofthedays,shesells4pies,andontheremaining55%ofthedays,shesellsallsixpies.IfMamaTemte
sellsherpiesfor$6each,whatisherexpectedprofitforadayʹsworthofpies?[Assumethatanyleftoverpies
aregivenaway.]
A) $16.80 B) $28.80 C) –$6.00 D) –$7.20
Page192
3) Alocalbakeryhasdeterminedaprobabilitydistributionforthenumberofcheesecakesthattheysellinagiven
day.Thedistributionisasfollows:
Numbersoldinaday 0510 15 20
Prob(Numbersold) 0.07 0.1 0.22 0.23 0.38
Findthenumberofcheesecakesthatthislocalbakeryexpectstosellinaday.
A) 13.75 B) 13.82 C) 14.1 D) 10
4) Adicegameinvolvesthrowingthreediceandbettingononeofthesixnumbersthatareonthedice.Thegame
costs$6toplay,andyouwinifthenumberyoubetappearsonanyofthedice.Thedistributionforthe
outcomesofthegame(includingtheprofit)isshownbelow:
Numberofdicewithyournumber Profit ProbabilityofObserving
0–$6 125/216
1$6 75/216
2$8 15/216
3$18 1/216
Findyourexpectedprofitfromplayingthisgame.
A) –$0.77 B) $0.50 C) $6.18 D) $3.39
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
5) Alegendaryfootballcoachwasknownforhiswinningseasons.Heconsistentlywonnineormoregamesper
season.Supposexequalsthenumberofgameswonuptothehalfwaymark(sixgames)ina12–gameseason.If
thiscoachandhisteamhadaprobabilityp=0.75ofwinninganyonegame(andthewinningorlosingofone
gamewasindependentofanother),thentheprobabilitydistributionofthenumberxofwinninggamesina
seriesofsixgamesis:
x P(x)
0 0.000244
1 0.004395
2 0.032959
3 0.131836
4 0.296631
5 0.355957
6 0.177979
Findtheexpectednumberofwinninggamesinthefirsthalfoftheseasonforthiscoachʹsfootballteams.
6) Ononebusyholidayweekend,anationalairlinehasmanyrequestsforstandbyflightsathalfoftheusual
one–wayairfare.However,pastexperiencehasshownthatthesepassengershaveonlyabouta1in5chanceof
gettingonthestandbyflight.Whentheyfailtogetonaflightasastandby,theironlyotherchoiceistoflyfirst
classonthenextflightout.Supposethattheusualone–wayairfaretoacertaincityis$142andthecostof
flyingfirstclassis$395.Shouldapassengerwhowishestoflytothiscityopttoflyasastandby?[Hint:Find
theexpectedcostofthetripforapersonflyingstandby.]
7) Anautomobileinsurancecompanyestimatesthefollowinglossprobabilitiesforthenextyearona$25,000
sportscar:
Totalloss: 0.001
50%loss: 0.01
25%loss: 0.05
10%loss: 0.10
Assumingthecompanywillsellonlya$500deductiblepolicyforthismodel(i.e.,theownercoversthefirst
$500damage),howmuchannualpremiumshouldthecompanychargeinordertoaverage$325profitper
policysold?
Page193
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
8) TrueorFalse:Theexpectedvalueofadiscreteprobabilitydistributionmaybenegative.
A) True B) False
9) Inacarnivalgame,apersonwagers$2ontherolloftwodice.Ifthetotalofthetwodiceis2,3,4,5,or6then
thepersongets$4(the$2wagerand$2winnings).Ifthetotalofthetwodiceis8,9,10,11,or12thenthe
persongetsnothing(loses$2).Ifthetotalofthetwodiceis7,thepersongets$0.75back(loses$0.25).Whatis
theexpectedvalueofplayingthegameonce?
A) –$0.04 B) –$0.42 C) $2.00 D) $0.00
10) IntheAmericanversionoftheGameRoulette,awheelhas18blackslots,8redslotsand2greenslots.Allslots
arethesamesize.Inacarnivalgame,apersonwagers$2ontherolloftwodice.Apersoncanwageroneither
redorblack.Greenisreservedforthehouse.Ifaplayerwagers$5oneitherredorblackandthatcolorcomes
up,theywin$10otherwisetheylosetheirwager.Whatistheexpectedvalueofplayingthegameonce?
A) –$0.26 B) –$0.50 C) $0.26 D) $0.50
6 Computethestandarddeviationofadiscreterandomvariable.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Therandomvariablexrepresentsthenumberofgirlsinafamilyofthreechildren.Assumingthatboysand
girlsareequallylikely,findthemeanandstandarddeviationfortherandomvariablex.
A) mean:1.50;standarddeviation:0.87 B) mean:2.25;standarddeviation:0.87
C) mean:1.50;standarddeviation:0.76 D) mean:2.25;standarddeviation:0.76
2) Therandomvariablexrepresentsthenumberofteststhatapatiententeringaclinicwillhavealongwiththe
correspondingprobabilities.Findthemeanandstandarddeviationfortherandomvariablex.
xP(x)
03
17
15
17
26
17
32
17
41
17
A) mean:1.59;standarddeviation:1.09 B) mean:1.59;standarddeviation:3.72
C) mean:2.52;standarddeviation:1.93 D) mean:3.72;standarddeviation:2.52
3) Therandomvariablexrepresentsthenumberofcomputersthatfamilieshavealongwiththecorresponding
probabilities.Findthemeanandstandarddeviationfortherandomvariablex.
x P(x)
0 0.49
1 0.05
2 0.32
3 0.07
40.07
A) mean:1.18;standarddeviation:1.30 B) mean:1.39;standarddeviation:0.64
C) mean:1.39;standarddeviation:0.80 D) mean:1.18;standarddeviation:0.64
Page194
4) Inasandwichshop,thefollowingprobabilitydistributionwasobtained.Therandomvariablexrepresentsthe
numberofcondimentsusedforahamburger.Findthemeanandstandarddeviationfortherandomvariablex.
x P(x)
0 0.30
1 0.40
2 0.20
3 0.06
40.04
A) mean:1.14;standarddeviation:1.04 B) mean:1.54;standarddeviation:1.30
C) mean:1.30;standarddeviation:2.38 D) mean:1.30;standarddeviation:1.54
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
5) Fromtheprobabilitydistribution,findthemeanandstandarddeviationfortherandomvariablex,which
representsthenumberofbicyclesperhouseholdinatownof1000households.
x P(x)
0 0.125
1 0.428
2 0.256
3 0.108
4 0.083
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
6) Abaseballplayerisaskedtoswingatpitchesinsetsoffour.Theplayerswingsat100setsof4pitches.The
probabilitydistributionforhittingaparticularnumberofpitchesisgivenbelow.Determinethestandard
deviationforthisdiscreteprobabilitydistribution.
x01234
P(x) 0.02 0.07 0.22 0.27 0.42
A) 1.05 B) 1.10 C) 1.21 D) 0.28
7) Theownerofafarmerʹsmarketwasinterestedindetermininghowmanyorangesapersonbuyswhenthey
buyoranges.Heaskedthecashiersoveraweekendtocounthowmanyorangesapersonboughtwhenthey
boughtorangesandrecordthisnumberforanalysisatalatertime.Thedataisgivenbelowinthetable.The
randomvariablexrepresentsthenumberoforangespurchasedandP(x)representstheprobabilitythata
customerwillbuyxoranges.Determinethevarianceofthenumberoforangespurchasedbyacustomer.
x12345678910
P(x) 0.05 0.19 0.20 0.25 0.12 0.10 0 0.08 0 0.01
A) 3.57 B) 1.95 C) 3.97 D) 0.56
8) Amanageratalocalcompanyaskedhisemployeeshowmanytimestheyhadgivenbloodinthelastyear.The
resultsofthesurveyaregivenbelow.Therandomvariablexrepresentsthenumberoftimesapersongave
bloodandP(x)representstheprobabilityofselectinganemployeewhohadgivenbloodthatpercentofthe
time.Whatisthestandarddeviationforthenumberoftimesapersongavebloodbasedonthissurvey?
x0123456
P(x) 0.30 0.25 0.20 0.12 0.07 0.04 0.02
A) 1.54 B) 1.82 C) 1.16 D) 2.23
Page195
9) Aseedcompanyhasatestplotinwhichitistestingthegerminationofahybridseed.Theyplant50rowsof40
seedsperrow.Afteratwo–weekperiod,theresearcherscounthowmanyseedperrowhavesprouted.They
notedthatleastnumberofseedstogerminatewas33andsomerowshadall40germinate.Thegermination
dataisgivenbelowinthetable.Therandomvariablexrepresentsthenumberofseedinarowthat
germinatedandP(x)representstheprobabilityofselectingarowwiththatnumberofseedgerminating.
Determinethestandarddeviationofthenumberofseedsperrowthatgerminated.
x33 34 35 36 37 38 39 40
P(x) 0.02 0.06 0.10 0.20 0.24 0.26 0.10 0.02
A) 1.51 B) 7.13 C) 36.86 D) 6.07
6.2 TheBinomialProbabilityDistribution
1 Determinewhetheraprobabilityexperimentisabinomialexperiment.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Youobservethegenderof
thenext850babiesbornatalocalhospital.Therandomvariablerepresentsthenumberofboys.
2) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Youdrawamarble350 times
fromabagwiththreecolorsofmarbles.Therandomvariablerepresentsthecolorofmarblethatisdrawn.
3) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Inagameyouspinawheel
thathas20differentletters1000times.Therandomvariablerepresentstheselectedletteroneachspinofthe
wheel.
4) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Testingacoughsuppressant
using820peopletodetermineifitiseffective.Therandomvariablerepresentsthenumberofpeoplewhofind
thecoughsuppressanttobeeffective.
5) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Survey450investorstosee
howmanydifferentstockstheyown.Therandomvariablerepresentsthenumberofdifferentstocksownedby
eachinvestor.
6) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Survey50collegestudents
seewhethertheyareenrolledasanewstudent.Therandomvariablerepresentsthenumberofstudents
enrolledasnewstudents.
7) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Eachweek,amanattendsa
clubmeetinginwhichhehasa37%chanceofmeetinganewmember.Therandomvariableisthenumberof
timeshemeetsanewmemberin30weeks.
8) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Youtestfourflumedicines.
Therandomvariablerepresentsthefluemedicinethatismosteffective.
9) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Eachweek,agamblerplays
blackjackatthelocalcasino.Therandomvariableisthenumberoftimesperweektheplayerwins.
10) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Selectingfivecards,oneata
timewithoutreplacement,fromastandarddeckofcards.Therandomvariableisthenumberofpicturecards
obtained.
Page196
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
11) TrueorFalse:Thetrialsofabinomialexperimentmustbemutuallyexclusiveofeachother.
A) False B) True
12) Whichofthebelowisnotarequirementforbinomialexperiment?
A) Thetrialsaremutuallyexclusive.
B) Theexperimentisperformedafixednumberoftimes.
C) Foreachtrialtherearetwomutuallyexclusiveoutcomes.
D) Theprobabilityofsuccessisfixedforeachtrialoftheexperiment.
13) Ifpistheprobabilityofsuccessofabinomialexperiment,thentheprobabilityoffailureis
A) 1–pB)
–pC)
x
nD) n
x
2 Computeprobabilitiesofbinomialexperiments.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Assumethatmaleandfemalebirthsareequallylikelyandthatthebirthofanychilddoesnotaffectthe
probabilityofthegenderofanyotherchildren.Findtheprobabilityofexactlyninegirlsintenbirths.
A) 0.010 B) 0.9 C) 0.020 D) 0.09
2) Inarecentsurvey,72%ofthecommunityfavoredbuildingahealthcenterintheirneighborhood.If14citizens
arechosen,findtheprobabilitythatexactly10ofthemfavorthebuildingofthehealthcenter.
A) 0.230 B) 0.001 C) 0.714 D) 0.720
3) Theprobabilitythatanindividualhas20–20vision is0.17.Inaclassof68 students,whatistheprobabilityof
findingfivepeoplewith20–20vision?
A) 0.012 B) 0.074 C) 0.000 D) 0.17
4) Accordingtoinsurancerecordsacarwithacertainprotectionsystemwillberecovered87%ofthetime.Find
theprobabilitythat4of10stolencarswillberecovered.
A) 0.001 B) 0.400 C) 0.87 D) 0.13
5) Theprobabilitythatafootballgamewillgointoovertimeis15%.Whatistheprobabilitythattwoofthree
footballgameswillgotointoovertime?
A) 0.057 B) 0.15 C) 0.325 D) 0.0225
6) FiftypercentofthepeoplethatusetheInternetordersomethingonline.Findtheprobabilitythatonlyfive of8
Internetuserswillordersomethingonline.
A) 0.219 B) 0.625 C) 0.004 D) 1.750
7) Theprobabilitythatahouseinanurbanareawilldevelopaleakis4%.If39 housesarerandomlyselected,
whatistheprobabilitythatnoneofthehouseswilldevelopaleak?
A) 0.204 B) 0.040 C) 0.000 D) 0.001
8) Sixty–fivepercentofmenconsiderthemselvesknowledgeablesoccerfans.If10 menarerandomlyselected,
findtheprobabilitythatexactlythreeofthemwillconsiderthemselvesknowledgeablefans.
A) 0.021 B) 0.252 C) 0.65 D) 0.300
9) Assumethatmaleandfemalebirthsareequallylikelyandthatthebirthofanychilddoesnotaffectthe
probabilityofthegenderofanyotherchildren.Findtheprobabilityofatmostthreegirlsintenbirths.
A) 0.172 B) 0.300 C) 0.003 D) 0.333
Page197
10) Aquizconsistsof10trueorfalsequestions.Topassthequizastudentmustansweratleasteightquestions
correctly.Ifthestudentguessesoneachquestion,whatistheprobabilitythatthestudentwillpassthequiz?
A) 0.055 B) 0.8 C) 0.20 D) 0.08
11) Aquizconsistsof10multiplechoicequestions,eachwithfivepossibleanswers,oneofwhichiscorrect.To
passthequizastudentmustget60%orbetteronthequiz.Ifastudentrandomlyguesses,whatisthe
probabilitythatthestudentwillpassthequiz?
A) 0.006 B) 0.060 C) 0.377 D) 0.205
12) Arecentsurveyfoundthat70%ofalladultsover50wearsunglassesfordriving.Inarandomsampleof10
adultsover50,whatistheprobabilitythatatleastsixwearsunglasses?
A) 0.850 B) 0.700 C) 0.200 D) 0.006
13) Accordingtogovernmentdata,theprobabilitythatanadultwasneverinamuseumis15%.Inarandom
surveyof10adults,whatistheprobabilitythattwoorfewerwereneverinamuseum?
A) 0.820 B) 0.002 C) 0.800 D) 0.200
14) Accordingtogovernmentdata,theprobabilitythatanadultwasneverinamuseumis15%.Inarandom
surveyof10adults,whatistheprobabilitythatatleasteightwereinamuseum?
A) 0.820 B) 0.200 C) 0.002 D) 0.800
15) AccordingtotheFederalCommunicationsCommission,70%ofallU.S.householdshavevcrs.Inarandom
sampleof15households,whatistheprobabilitythatatleast13havevcrs?
A) 0.1268 B) 0.7 C) 0.8732 D) 0.5
16) AccordingtotheFederalCommunicationsCommission,70%ofallU.S.householdshavevcrs.Inarandom
sampleof15households,whatistheprobabilitythatthenumberofhouseholdswithvcrsisbetween10and12,
inclusive?
A) 0.5947 B) 0.4053 C) 0.7 D) 0.2061
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
17) Amotelhasapolicyofbookingasmanyas150guestsinabuildingthatholds140.Paststudiesindicatethat
only85%ofbookedguestsshowupfortheirroom.Findtheprobabilitythatifthemotelbooks150guests,not
enoughseatswillbeavailable.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
18) Webelievethat86%ofthepopulationofallCalculusIstudentsconsidercalculusanexcitingsubject.Suppose
werandomlyandindependentlyselected29studentsfromthepopulation.Ifthetruepercentageisreally86%,
findtheprobabilityofobserving28ormoreofthestudentswhoconsidercalculustobeanexcitingsubjectin
oursampleof29.
A) 0.072098 B) 0.012602 C) 0.059495 D) 0.927902
19) Apsychicnetworkreceivedtelephonecallslastyearfromover1.5millionpeople.Arecentarticleattemptsto
shedsomelightontothecredibilityofthepsychicnetwork.Oneofthepsychicnetworkʹspsychicsagreedto
takepartinthefollowingexperiment.Fivedifferentcardsareshuffled,andoneischosenatrandom.The
psychicwillthentrytoidentifywhichcardwasdrawnwithoutseeingit.Assumethattheexperimentwas
repeated50timesandthattheresultsofanytwoexperimentsareindependentofoneanother.Ifweassume
thatthepsychicisafake(i.e.,theyaremerelyguessingatthecardsandhavenopsychicpowers),findthe
probabilitythattheyguessatleastthreecorrectly.
A) 0.998715 B) 0.001257 C) 0.004371 D) 0.001093
Page198
20) Ahistoryprofessordecidestogivea12–questiontrue–falsequiz.Shewantstochoosethepassinggradesuch
thattheprobabilityofpassingastudentwhoguessesoneveryquestionislessthan0.10.Whatscoreshouldbe
setasthelowestpassinggrade?
A) 9 B) 7 C) 10 D) 8
21) Arecentarticleinthepaperclaimsthatgovernmentethicsareatanall–timelow.Reportingonarecentsample,
thepaperclaimsthat38%ofallconstituentsbelievetheirrepresentativepossesseslowethicalstandards.
Assumethatresponseswererandomlyandindependentlycollected.Arepresentativeofadistrictwith1,000
peopledoesnotbelievethepaperʹsclaimappliestoher.Iftheclaimistrue,howmanyoftherepresentativeʹs
constituentsbelievetherepresentativepossesseslowethicalstandards?
A) 380 B) 38 C) 620 D) 962
22) Arecentarticleinthepaperclaimsthatgovernmentethicsareatanall–timelow.Reportingonarecentsample,
thepaperclaimsthat45%ofallconstituentsbelievetheirrepresentativepossesseslowethicalstandards.
Suppose20ofarepresentativeʹsconstituentsarerandomlyandindependentlysampled.Assumingthepaperʹs
claimiscorrect,findtheprobabilitythatmorethaneightbutfewerthan12ofthe20constituentssampled
believetheirrepresentativepossesseslowethicalstandards.
A) 0.454929 B) 0.295579 C) 0.689728 D) 0.889609
3 Computethemeanandstandarddeviationofabinomialrandomvariable.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Assumethatmaleandfemalebirthsareequallylikelyandthatthebirthofanychilddoesnotaffectthe
probabilityofthegenderofanyotherchildren.Supposethat200coupleseachhaveababy;findthemeanand
standarddeviationforthenumberofboysinthe200babies.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
2) Aquizconsistsof920trueorfalsequestions.Ifthestudentguessesoneachquestion,whatisthemeannumber
ofcorrectanswers?
A) 460 B) 0 C) 920 D) 184
3) Aquizconsistsof780trueorfalsequestions.Ifthestudentguessesoneachquestion,whatisthestandard
deviationofthenumberofcorrectanswers?
A) 13.96424 B) 0 C) 2 D) 19.7484177
4) Aquizconsistsof50multiplechoicequestions,eachwithfivepossibleanswers,onlyoneofwhichiscorrect.
Findthemeanandthestandarddeviationofthenumberofcorrectanswers.
A) mean:10;standarddeviation:2.82842712 B) mean:10;standarddeviation:3.16227766
C) mean:25;standarddeviation:2.82842712 D) mean:25;standarddeviation:5
5) Theprobabilitythatanindividualhas20–20vision is0.1.Inaclassof10 students,whatisthemeanand
standarddeviationofthenumberwith20–20visionintheclass?
A) mean:1;standarddeviation:0.9486833 B) mean:10;standarddeviation:0.9486833
C) mean:1;standarddeviation:1 D) mean:10;standarddeviation:1
6) Arecentsurveyfoundthat69%ofalladultsover50wearsunglassesfordriving.Inarandomsampleof20
adultsover50,whatisthemeanandstandarddeviationofthosethatwearsunglasses?
A) mean:13.8;standarddeviation:2.06833266 B) mean:13.8;standarddeviation:3.71483512
C) mean:6.2;standarddeviation:2.06833266 D) mean:6.2;standarddeviation:3.71483512
Page199
7) Accordingtogovernmentdata,theprobabilitythatanadultwasneverinamuseumis20%.Inarandom
surveyof70adults,whatisthemeanandstandarddeviationofthenumberthatwereneverinamuseum?
A) mean:14;standarddeviation:3.34664011 B) mean:56 standarddeviation:3.74165739
C) mean:56;standarddeviation:3.34664011 D) mean:14;standarddeviation:3.74165739
8) Accordingtoinsurancerecords,acarwithacertainprotectionsystemwillberecovered92%ofthetime.If800
stolencarsarerandomlyselected,whatisthemeanandstandarddeviationofthenumberofcarsrecovered
afterbeingstolen?
A) mean:736;standarddeviation:7.67333044 B) mean:736;standarddeviation:58.88
C) mean:–5664:standarddeviation:7.67333044 D) mean:–5664:standarddeviation:58.88
9) Theprobabilitythatafootballgamewillgointoovertimeis15%.In260 randomlyselectedfootballgames,
whatisthemeanandthestandarddeviationofthenumberthatwentintoovertime?
A) mean:39;standarddeviation:5.75760367 B) mean:39;standarddeviation:6.244998
C) mean:36.4;standarddeviation:5.75760367 D) mean:36.4;standarddeviation:6.244998
10) Inarecentsurvey,80%ofthecommunityfavoredbuildingahealthcenterintheirneighborhood.If15citizens
arechosen,whatisthemeannumberfavoringthehealthcenter?
A) 12 B) 15 C) 8 D) 10
11) Inarecentsurvey,80%ofthecommunityfavoredbuildingahealthcenterintheirneighborhood.If15citizens
arechosen,whatisthestandarddeviationofthenumberfavoringthehealthcenter?
A) 1.55 B) 2.40 C) 0.98 D) 0.55
12) Theprobabilitythatahouseinanurbanareawilldevelopaleakis5%.If20housesarerandomlyselected,
whatisthemeanofthenumberofhousesthatdevelopedleaks?
A) 1 B) 2 C) 0.5 D) 1.5
13) Apsychicnetworkreceivedtelephonecallslastyearfromover1.5millionpeople.Arecentarticleattemptsto
shedsomelightontothecredibilityofthepsychicnetwork.Oneofthepsychicnetworkʹspsychicsagreedto
takepartinthefollowingexperiment.Fivedifferentcardsareshuffled,andoneischosenatrandom.The
psychicwillthentrytoidentifywhichcardwasdrawnwithoutseeingit.Assumethattheexperimentwas
repeated45timesandthattheresultsofanytwoexperimentsareindependentofoneanother.Ifweassume
thatthepsychicisafake(i.e.,theyaremerelyguessingatthecardsandhavenopsychicpowers),howmanyof
the45cardsdoweexpectthepsychictoguesscorrectly?
A) 9 B) 8 C) 0 D) 5
4 Constructbinomialprobabilityhistograms.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Drawtheprobabilityhistogramandlabelthemeanforn=6andp=0.4
2) Drawtheprobabilityhistogramandlabelthemeanforn=7andp=0.5
3) Drawtheprobabilityhistogramandlabelthemeanforn=8andp=0.3
4) Drawtheprobabilityhistogramandlabelthemeanforn=9andp=0.7
Page200
6.3 ThePoissonProbabilityDistribution
1 DetermineifaprobabilityexperimentfollowsaPoissonprocess.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Giventhatarandomvariablex,thenumberofsuccesses,followsaPoissonprocess,theprobabilityof2ormore
successesinanysufficientlysmallsubintervalis
A) zero. B) one.
C) anynumberbetweenzeroandone. D) noneofthese
2) Giventhatarandomvariablex,thenumberofsuccesses,followsaPoissonprocess,thentheprobabilityof
successforanytwointervalsofthesamesize
A) isthesame. B) arecomplementary.
C) arereciprocals. D) noneofthese
3) Giventhatarandomvariablex,thenumberofsuccesses,followsaPoissonprocess,thenthenumberof
successesinanyintervalisindependentofthenumberofsuccessesinanyotherintervalprovidedtheintervals
A) aredisjoint. B) overlap.
C) haveatleastoneelementincommon. D) arethesamesizeandareindependent.
2 ComputeprobabilitiesofaPoissonrandomvariable.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Ahistoryprofessorfindsthatwhenheschedulesanofficehouratthe10:30a.m.timeslot,anaverageofthree
studentsarrive.UsethePoissondistributiontofindtheprobabilitythatinarandomlyselectedofficehourin
the10:30a.m.timeslotexactlysevenstudentswillarrive.
A) 0.0216 B) 0.0004 C) 0.0034 D) 0.0001
2) Ahelpdeskreceivesanaverageoffourcallsperhouronitstoll–freenumber.Foranygivenhour,findthe
probabilitythatitwillreceiveexactlysixcalls.UsethePoissondistribution.
A) 0.1042 B) 0.0141 C) 725.7202 D) 0.0330
3) Thelocalpolicedepartmentreceivesanaverageof twocallsperhour.UsethePoissondistributionto
determinetheprobabilitythatinarandomlyselectedhourthenumberofcallsisfive.
A) 0.0361 B) 0.0018 C) 0.0282 D) 0.0014
4) Adictionarycontains500pages.Ifthereare200typingerrorsrandomlydistributedthroughoutthebook,use
thePoissondistributiontodeterminetheprobabilitythatapagecontainsexactlythreeerrors.
A) 0.0072 B) 0.0005 C) 0.1734 D) 0.0129
5) Acustomerservicefirmreceivesanaverageofthreecallsperhouronitstoll–freenumber.Foranygivenhour,
findtheprobabilitythatitwillreceiveatleastthreecalls.UsethePoissondistribution.
A) 0.5768 B) 0.1891 C) 0.4232 D) 0.6138
6) Anonlineretailerreceivesanaverageoffiveordersper500hitsonitswebsite.Ifitgets100hitsonitswebsite,
findtheprobabilityofreceivingatleasttwoorders.UsethePoissondistribution.
A) 0.2642 B) 0.1839 C) 0.9048 D) 0.9596
Page201
7) Alocalanimalrescueorganizationreceivesanaverageof0.55rescuecallsperhour.UsethePoisson
distributiontofindtheprobabilitythatduringarandomlyselectedhour,theorganizationwillreceivefewer
thantwocalls.
A) 0.894 B) 0.106 C) 0.317 D) 0.087
8) ThenumberofroadconstructionprojectsthattakeplaceatanyonetimeinacertaincityfollowsaPoisson
distributionwithameanof5.Findtheprobabilitythatexactlysixroadconstructionprojectsarecurrently
takingplaceinthiscity.
A) 0.146223 B) 0.322754 C) 0.072770 D) 0.160623
9) ThenumberofroadconstructionprojectsthattakeplaceatanyonetimeinacertaincityfollowsaPoisson
distributionwithameanof6.Findtheprobabilitythatmorethanfourroadconstructionprojectsarecurrently
takingplaceinthecity.
A) 0.714943 B) 0.848796 C) 0.285057 D) 0.151204
10) ThenumberoftrafficaccidentsthatoccuronaparticularstretchofroadduringamonthfollowsaPoisson
distributionwithameanof7.2.Findtheprobabilitythatlessthanthreeaccidentswilloccurnextmonthonthis
stretchofroad.
A) 0.025474 B) 0.071917 C) 0.974526 D) 0.928083
11) ThenumberoftrafficaccidentsthatoccuronaparticularstretchofroadduringamonthfollowsaPoisson
distributionwithameanof7.5.Findtheprobabilityofobservingexactlyfiveaccidentsonthisstretchofroad
nextmonth.
A) 0.109375 B) 1.332455 C) 0.805166 D) 9.808925
12) ThenumberoftrafficaccidentsthatoccuronaparticularstretchofroadduringamonthfollowsaPoisson
distributionwithameanof6.3.Findtheprobabilitythatthenexttwomonthswillbothresultinfiveaccidents
eachoccurringonthisstretchofroad.
A) 0.023064 B) 0.151868 C) 0.303736 D) 0.008924
13) Supposethenumberofbabiesbornduringan8–hourshiftatahospitalʹsmaternitywingfollowsaPoisson
distributionwithameanof5anhour.Findtheprobabilitythatthreebabiesarebornduringaparticular
1–hourperiodinthismaternitywing.
A) 0.140374 B) 0.021780 C) 0.017547 D) 0.002053
14) Supposethenumberofbabiesbornduringan8–hourshiftatahospitalʹsmaternitywingfollowsaPoisson
distributionwithameanof2anhour.Somepeoplebelievethatthepresenceofafullmoonincreasesthe
numberofbirthsthattakeplace.Supposeduringthepresenceofafullmoon,CountyHospitalexperienced
eightconsecutivehourswithmorethanthreebirths.Basedonthisfact,commentonthebeliefthatthefull
moonincreasesthenumberofbirths.
A) Thebeliefissupportedastheprobabilityofobservingthismanybirthswouldbe0.000000175.
B) Thebeliefisnotsupportedastheprobabilityofobservingthismanybirthsis0.143.
C) Thebeliefissupportedastheprobabilityofobservingthismanybirthswouldbe0.143.
D) Thebeliefisnotsupportedastheprobabilityofobservingthismanybirthsis0.000000175.
15) Theuniversitypolicedepartmentmustwrite,onaverage,fiveticketsperdaytokeepdepartmentrevenuesat
budgetedlevels.SupposethenumberofticketswrittenperdayfollowsaPoissondistributionwithameanof
9.6ticketsperday.Findtheprobabilitythatlessthansixticketsarewrittenonarandomlyselecteddayfrom
thisdistribution.
A) 0.083815 B) 0.157447 C) 0.916185 D) 0.842553
Page202
16) Theuniversitypolicedepartmentmustwrite,onaverage,fiveticketsperdaytokeepdepartmentrevenuesat
budgetedlevels.SupposethenumberofticketswrittenperdayfollowsaPoissondistributionwithameanof5
ticketsperday.Findtheprobabilitythatexactlyeightticketsarewrittenonarandomlyselecteddayfromthis
distribution.
A) 0.065278 B) 0.005476 C) 0.003250 D) 0.000273
17) ThenumberofgoalsscoredatStateCollegehockeygamesfollowsaPoissondistributionwithameanof4
goalspergame.FindtheprobabilitythatarandomlyselectedStateCollegehockeygamewouldhavemore
thanthreegoalsscored.
A) 0.566530 B) 0.433470 C) 0.761897 D) 0.238103
18) ThenumberofgoalsscoredatStateCollegehockeygamesfollowsaPoissondistributionwithameanof4
goalspergame.FindtheprobabilitythateachofthreerandomlyselectedStateCollegehockeygamesresulted
insevengoalsbeingscored.
A) 0.00021107 B) 0.17862110 C) 0.00001086 D) 0.82137890
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
19) Asmalllifeinsurancecompanyhasdeterminedthatontheaverageitreceives3 deathclaimsperday.Findthe
probabilitythatthecompanyreceivesatleastsevendeathclaimsonarandomlyselectedday.
20) ThenumberoftrafficaccidentsthatoccursonaparticularstretchofroadduringamonthfollowsaPoisson
distributionwithameanof6.3.Findtheprobabilitythatlessthantwoaccidentswilloccuronthisstretchof
roadduringarandomlyselectedmonth.
21) Supposethenumberofbabiesbornduringaneight–hourshiftatahospitalʹsmaternitywingfollowsaPoisson
distributionwithameanof6anhour.Findtheprobabilitythatexactlyfourbabiesarebornduringarandomly
selectedhour.
3 FindthemeanandstandarddeviationofaPoissonrandomvariable.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Theuniversitypolicedepartmentmustwrite,onaverage,fiveticketsperdaytokeepdepartmentrevenuesat
budgetedlevels.SupposethenumberofticketswrittenperdayfollowsaPoissondistributionwithameanof
6.5ticketsperday.Interpretthevalueofthemean.
A) Ifwesampledalldays,thearithmeticaveragenumberofticketswrittenwouldbe6.5ticketsperday.
B) Thenumberofticketsthatiswrittenmostoftenis6.5 ticketsperday.
C) Halfofthedayshavelessthan6.5 ticketswrittenandhalfofthedayshavemorethan6.5ticketswritten.
D) Themeanhasnointerpretationsince0.5ticketcanneverbewritten.
2) SupposexisarandomvariableforwhichaPoissonprobabilitydistributionwithλ
=8.7providesagood
characterization.Findμforx.
A) 8.7 B) 2.95 C) 4.4 D) 75.69
3) SupposexisarandomvariableforwhichaPoissonprobabilitydistributionwithλ
=1.2 providesagood
characterization.Findσforx.
A) 1.1 B) 1.2 C) 0.6 D) 1.44
4) ThenumberofgoalsscoredatStateCollegesoccergamesfollowsaPoissonprocesswithagoalscored
approximatelyevery18minutes(asoccergameconsistsof245 –minutehalves).Whatisthemeannumberof
goalsscoredduringagame
A) 5 B) 2.5 C) 0.11 D) 1.25
Page203
5) ThenumberofgoalsscoredatStateCollegesoccergamesfollowsaPoissonprocesswithagoalscored
approximatelyevery18minutes(asoccergameconsistsof245 –minutehalves).Whatisthestandard
deviationofthemeannumberofgoalsscoredduringagame?
A) 2.34 B) 1.58 C) 1.12 D) 1.27
6) Theuniversitypolicedepartmentkeepstrackofthenumberofticketsitwriteinayear.Lastyearthecampus
policewrote1460tickets.TicketwritingoncampusfollowsaPoissonprocess.Whatisthemeannumberof
ticketswrittenperdaybythecampuspolice?
A) 4 B) 2 C) 6.08 D) 5
7) Theuniversitypolicedepartmentkeepstrackofthenumberofticketsitwriteinayear.Lastyearthecampus
policewrote1460tickets.TicketwritingoncampusfollowsaPoissonprocess.Whatisthestandarddeviation
ofthenumberofticketswrittenperdaybythecampuspolice?
A) 2 B) 1.4 C) 2.47 D) 1.73
6.4 TheHypergeometricProbabilityDistribution(onCD)
1 Determinewhetheraprobabilityexperimentisahypergeometricexperiment.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Determinewhethertheprobabilityexperimentrepresentsahypergeometricprobabilityexperiment.Ifitdoes,
determinethevaluesofN,n,andkandlistthepossiblevaluesoftherandomvariableX.
1) Ajuryistobeselectedfromapoolof34 potentialjurors.Thedefendantfacesthedeathpenaltyifconvicted.Of
thepotentialjurors,7areopposedtothedeathpenalty.Thejuryconsistsof12randomlyselectedjurors.The
randomvariableXrepresentsthenumberofjurorswhoopposethedeathpenalty.
A) hypergeometric;N=34
,
n=12,k=7,x=0,1,2,...,7
B) hypergeometric;N=34
,
n=7,k=12,x=0,1,2,...,7
C) hypergeometric;N=34
,
n=12,k=7,x=0,1,2,...,12
D) nothypergeometric
2) Anelectronicsstorereceivesashipmentof50 flatscreenTVsofwhich5 aredefective.Duringthequality
controlinspection,4TVsareselectedatrandomfromtheshipmentfortesting.TherandomvariableX
representsthenumberofdefectivecomputersinthesample
A) hypergeometric;N=50
,
n=4,k=5
,
x=0,1,2,3,4
B) hypergeometric;N=50
,
n=5
,
k=4,x=0,1,2,3,4
C) hypergeometric;N=50
,
n=4,k=5
,
x=0,1,2,...,5
D) nothypergeometric
3) Auniversitymustchooseateamof5studentstoparticipateinaTVquizshow.Thestudentswillbechosenat
randomfromapoolof44potentialparticipantsofwhom20arewomen.TherandomvariableXrepresentsthe
numberofwomenontheteam.
A) hypergeometric;N=44
,
n=5,k=20
,
x=0,1,2,3,4,5
B) hypergeometric;N=44
,
n=20
,
k=5,x=0,1,2,3,4,5
C) hypergeometric;N=44
,
n=5,k=20
,
x=0,1,2,...,20
D) nothypergeometric
4) Ofthe3800studentsatacollege,280arematurestudents.50studentsareselectedatrandomfromthe3800
studentsatthecollegeandaskedtoparticipateinasurvey.Thequestionsinthesurveyrelatetothestudentʹs
needforfinancialassistance.TherandomvariableXrepresentsthenumberofmaturestudentsinthesample.
A) hypergeometric;N=3800,n=50,k=280,x=0,1,2,...,50
B) hypergeometric;N=3800,n=280,k=50,x=0,1,2,...,50
C) hypergeometric;N=3800,n=50,k=280,x=0,1,2,...,280
D) nothypergeometric
Page204
2 Computetheprobabilitiesofhypergeometricexperiments.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Ahypergeometricprobabilityexperimentisconductedwiththegivenparameters.Computetheprobabilityof
obtainingxsuccesses.
N=130,n=10,k=25,x=3
A) 0.1965 B) 0.1914 C) 0.1867 D) 0.1722
2) Amanufacturerreceivesashipmentof170 laptopcomputersofwhich11 aredefective.Totesttheshipment,
thequalitycontrolengineerrandomlyselects20computersfromtheshipmentandteststhem.Therandom
variableXrepresentsthenumberofdefectivecomputersinthesample.Whatistheprobabilityofobtaining3
defectivecomputers?
A) 0.0971 B) 0.0991 C) 0.0891 D) 0.0923
3) Auniversitymustchooseateamof6studentstoparticipateinaTVquizshow.Thestudentswillbechosen
fromapoolof32potentialparticipantsofwhom14arewomen.Ifthe6studentsarechosenatrandom,whatis
theprobabilitythattheteamwillcontain2women?
A) 0.3073 B) 0.2766 C) 0.2874 D) 0.2587
Solvetheproblem.
4) Inalottery,aplayerselectssixnumbersbetween1and36 inclusive.Thesixwinningnumbers(alldifferent)are
selectedatrandomfromthenumbers1–36.Towinaprize,theplayermustmatchthreeormoreofthewinning
numbers.Whatistheprobabilitythattheplayermatchesexactly3numbers?
A) 0.0417 B) 0.0347 C) 0.0486 D) 0.0521
5) Anelectronicsstorereceivesashipmentof59 flatscreenTVsofwhich6 aredefective.Duringthequality
controlinspection,3TVsareselectedatrandomfromtheshipmentfortesting.Theshipmentwillonlybe
acceptedifall3TVspasstheinspection.Whatistheprobabilitythattheshipmentwillbeaccepted?
A) 0.7206 B) 0.7249 C) 0.0011 D) 0.0006
6) AIRSauditorrandomlyselects3taxreturnsfrom42 returnsofwhich15 containerrors.Whatistheprobability
thatnoneofthereturnssheselectscontainsanerror?
A) 0.2548 B) 0.2657 C) 0.0456 D) 0.0396
7) Amongthecontestantsinacompetitionare35 womenand20 men.If5winnersarerandomlyselected,whatis
theprobabilitythattheyareallmen?
A) 0.00446 B) 0.04776 C) 0.10436 D) 0.06093
Provideanappropriateresponse.
8) Ajuryistobeselectedfromapoolof40 potentialjurors.Thedefendantfacesthedeathpenaltyifconvicted.Of
thepotentialjurors,5areopposedtothedeathpenaltyandwouldnotconvictregardlessoftheevidence.The
prosecutorknowsthatifevenonejuroropposesthedeathpenalty,theywillhavenochanceofgettinga
conviction.Ifnoneofthejurorsopposesthedeathpenaltytheywillhaveachanceofgettingaconviction.What
istheprobabilitythatnoneofthejurorsopposesthedeathpenalty,ifthejuryconsistsof12randomlyselected
jurors?
A) 0.1494 B) 0.1643 C) 0.2014 D) 0.1813
Page205
3 Computethemeanandstandarddeviationofahypergeometricrandomvariable.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
ComputethemeanandstandarddeviationofthehypergeometricrandomvariableX.
1) N=130
,
n=10
,
k=35
A) μX=2.69
,
σX=1.35 B) μX=2.69
,
σX=1.40
C) μX=0.27
,
σX=1.35 D) μX=2.42
,
σX=1.40
2) Inalottery,aplayermustchoose6numbersbetween1and48 inclusive.Sixballsarethenrandomlyselected
fromanurncontaining48ballsnumberedfrom1to48.TherandomvariableXrepresentsthenumberof
matchingnumbers.WhatarethemeanandstandarddeviationoftherandomvariableX?
A) μX=0.750
,
σX=35.992 B) μX=0.750
,
σX=0.810
C) μX=0.125
,
σX=35.992 D) μX=0.125
,
σX=0.810
3) Amanufacturerreceivesashipmentof170 laptopcomputersofwhich9 aredefective.Totesttheshipment,the
qualitycontrolengineerrandomlyselects10computersfromtheshipmentandteststhem.Therandom
variableXrepresentsthenumberofdefectivecomputersinthesample.Whatarethemeanandstandard
deviationoftherandomvariableX?
A) μX=0.529
,
σX=0.689 B) μX=0.529
,
σX=0.708
C) μX=0.053
,
σX=0.689 D) μX=0.529
,
σX=0.475
Page206
Ch.6 DiscreteProbabilityDistributions
AnswerKey
6.1 DiscreteRandomVariables
1 Distinguishbetweendiscreteandcontinuousrandomvariables.
2 Identifydiscreteprobabilitydistributions.
Page207
3 Constructprobabilityhistograms.
Page208
Page209
4 Computeandinterpretthemeanofadiscreterandomvariable.
5 Interpretthemeanofadiscreterandomvariableasanexpectedvalue.
Page210
6 Computethestandarddeviationofadiscreterandomvariable.
6.2 TheBinomialProbabilityDistribution
1 Determinewhetheraprobabilityexperimentisabinomialexperiment.
2 Computeprobabilitiesofbinomialexperiments.
Page211
3 Computethemeanandstandarddeviationofabinomialrandomvariable.
4 Constructbinomialprobabilityhistograms.
Page212
Page213
6.3 ThePoissonProbabilityDistribution
1 DetermineifaprobabilityexperimentfollowsaPoissonprocess.
2 ComputeprobabilitiesofaPoissonrandomvariable.
Page214
3 FindthemeanandstandarddeviationofaPoissonrandomvariable.
6.4 TheHypergeometricProbabilityDistribution(onCD)
1 Determinewhetheraprobabilityexperimentisahypergeometricexperiment.
2 Computetheprobabilitiesofhypergeometricexperiments.
3 Computethemeanandstandarddeviationofahypergeometricrandomvariable.
Page215