Chapter 04 Attendance Discrete Attendance Random Variable That Countable

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Ch.4 DiscreteProbabilityDistributions

4.1 ProbabilityDistributions

1 DecideifaRandomVariableisDiscreteorContinuous

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Statewhetherthevariableisdiscreteorcontinuous.

Thenumberofcupsofcoffeesoldinacafeteriaduringlunch

A) discrete B) continuous

2) Statewhetherthevariableisdiscreteorcontinuous.

Theheightofaplayeronabasketballteam

A) continuous B) discrete

3) Statewhetherthevariableisdiscreteorcontinuous.

ThecostofaStatisticstextbook

A) discrete B) continuous

4) Statewhetherthevariableisdiscreteorcontinuous.

Thebloodpressuresofagroupofstudentsthedaybeforetheirfinalexam

A) continuous B) discrete

5) Statewhetherthevariableisdiscreteorcontinuous.

ThetemperatureindegreesFahrenheitonJuly4thinJuneau,Alaska

A) continuous B) discrete

6) Statewhetherthevariableisdiscreteorcontinuous.

Thenumberofgoalsscoredinasoccergame

A) discrete B) continuous

7) Statewhetherthevariableisdiscreteorcontinuous.

ThespeedofacaronaLosAngelesfreewayduringrushhourtraffic

A) continuous B) discrete

8) Statewhetherthevariableisdiscreteorcontinuous.

Thenumberofphonecallstotheattendanceofficeofahighschoolonanygivenschoolday

A) discrete B) continuous

9) Statewhetherthevariableisdiscreteorcontinuous.

Theageoftheoldeststudentinastatisticsclass

A) continuous B) discrete

10) Statewhetherthevariableisdiscreteorcontinuous.

Thenumberofpillsinacontainerofvitamins

A) discrete B) continuous

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11) Determinewhetherthenumberlinerepresentsadiscreterandomvariableoracontinuousrandomvariable.

Explainyourreasoning.

Theattendanceatgamesforasportsteam

15000 17500 20000 22500 25000

Attendance

15000 17500 20000 22500 25000

Attendance

A) Discrete;Attendanceisarandomvariablethatiscountable.

B) Continuous;Attendanceisarandomvariablethatmustbemeasured.

12) Determinewhetherthenumberlinerepresentsadiscreterandomvariableoracontinuousrandomvariable.

Explainyourreasoning.

Thelengthoftimecollegestudentsstudyeachweek

8 12162024

Time (in hours)

8 12162024

Time (in hours)

A) Continuous;Timeisarandomvariablethatmustbemeasured.

B) Discrete;Timeisarandomvariablethatiscountable.

2 FindProbabilities

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Therandomvariablexrepresentsthenumberofcarsperhouseholdinatownof1000households.Findthe

probabilityofrandomlyselectingahouseholdthathaslessthantwocars.

Cars Households

0125

1 428

2 256

3 108

483

A) 0.553 B) 0.809 C) 0.428 D) 0.125

2) Therandomvariablexrepresentsthenumberofcarsperhouseholdinatownof1000households.Findthe

probabilityofrandomlyselectingahouseholdthathasatleastonecar.

Cars Households

0 125

1 428

2 256

3 108

483

A) 0.875 B) 0.125 C) 0.500 D) 0.083

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3) Therandomvariablexrepresentsthenumberofcarsperhouseholdinatownof1000households.Findthe

probabilityofrandomlyselectingahouseholdthathasbetweenoneandthreecars,inclusive.

Cars Households

0 125

1 428

2 256

3 108

483

A) 0.792 B) 0.125 C) 0.208 D) 0.256

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

4) Astudenthasfivemotorvehicleaccidentsinoneyearandclaimsthathavingfiveaccidentsisnotunusual.

Usethefrequencydistributionbelowtodetermineifthestudentiscorrect.

Accidents 0 12345

Students 260 500 425 305 175 45

5) AbaseballplayergetsfourhitsduringtheWorldSeriesandasportsannouncerclaimsthatgettingfouror

morehitsisnotunusual.Usethefrequencydistributionbelowtodetermineifthesportsannounceriscorrect.

Hits 01234567

Players 79741121

3 ConstructProbabilityDistributions

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) AsportsanalystrecordsthewinnersofNASCARWinstonCupracesforarecentseason.Therandomvariable

xrepresentstheraceswonbyadriverinoneseason.Usethefrequencydistributiontoconstructaprobability

distribution.

Wins 1234567

Drivers 12 2 0 2 0 0 1

2) Aninsuranceactuaryaskedasampleofseniorcitizensthecauseoftheirautomobileaccidentsoveratwo –year

period.Therandomvariablexrepresentsthenumberofaccidentscausedbytheirfailuretoyieldtherightof

way.Usethefrequencydistributiontoconstructaprobabilitydistribution.

Accidents 012345

SeniorCitizens 4 3 12 3 2 1

3) AsportsannouncerresearchedtheperformanceofbaseballplayersintheWorldSeries.Therandomvariablex

representsthenumberofofhitsaplayerhadintheseries.Usethefrequencydistributiontoconstructa

probabilitydistribution.

Hits 01234567

Players 7 9 7 4 1 1 2 1

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MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

4) Determinetheprobabilitydistributionʹsmissingvalue.

Theprobabilitythatatutorwillsee0,1,2,3,or4students

x 01234

P(x) 007

17 ?5

A) 5

17 B) 6

17 C) 12

17 D) – 10

5) Determinetheprobabilitydistributionʹsmissingvalue.

Theprobabilitythatatutorwillsee0,1,2,3,or4students

x01234

P(x) 0.16 0.04 0.19 0.14 ?

A) 0.47 B) 0.8 C) 0.53 D) –0.67

6) Determinetheprobabilitydistributionʹsmissingvalue.

Theprobabilitythatatutorsees0,1,2,3,or4studentsonagivenday.

x 01234

P(x) ? 0.15 0.20 0.20 0.25

A) 0.20 B) 0.50 C) 0.80 D) 1.0

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

7) Therandomvariablexrepresentsthenumberofboysinafamilyofthreechildren.Assumingthatboysand

girlsareequallylikely,(a)constructaprobabilitydistribution,and(b)graphthedistribution.

8) Therandomvariablexrepresentsthenumberofteststhatapatiententeringahospitalwillhavealongwiththe

correspondingprobabilities.Graphtheprobabilitydistribution.

x01234

P(x) 3

9) Therandomvariablexrepresentsthenumberofcreditcardsthatadultshavealongwiththecorresponding

probabilities.Graphtheprobabilitydistribution.

xP(x)

0 0.07

1 0.68

2 0.21

3 0.03

4 0.01

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10) Inapizzatakeoutrestaurant,thefollowingprobabilitydistributionwasobtained.Therandomvariablex

representsthenumberoftoppingsforalargepizza.Graphtheprobabilitydistribution.

x P(x)

0 0.30

1 0.40

2 0.20

3 0.06

40.04

11) Usethefrequencydistributionto(a)constructaprobabilitydistributionfortherandomvariablexwhich

representsthenumberofcarsperhouseholdinatownof1000households,and(b)graphthedistribution.

Cars Households

0 125

1 428

2 256

3 108

483

4 DetermineifaDistributionisaProbabilityDistribution

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Determinewhetherthedistributionrepresentsaprobabilitydistribution.Ifnot,identifyanyrequirementsthat

arenotsatisfied.

x P(x)

1 0.2

2 0.2

3 0.2

4 0.2

5 0.2

2) Determinewhetherthedistributionrepresentsaprobabilitydistribution.Ifnot,identifyanyrequirementsthat

arenotsatisfied.

x P(x)

3–0.3

6 0.5

9 0.1

12 0.3

15 0.4

3) Determinewhetherthedistributionrepresentsaprobabilitydistribution.Ifnot,identifyanyrequirementsthat

arenotsatisfied.

x P(x)

1 1.2

2 1.2

3 1.4

4 1.1

5 1.1

Page94

4) Determinewhetherthedistributionrepresentsaprobabilitydistribution.Ifnot,identifyanyrequirementsthat

arenotsatisfied.

x P(x)

1 0.49

2 0.05

3 0.32

4 0.07

5 0.07

5) Determinewhetherthedistributionrepresentsaprobabilitydistribution.Ifnot,identifyanyrequirementsthat

arenotsatisfied.

x P(x)

1–0.2

2–0.2

3–0.2

4–0.2

5–0.2

5 FindtheExpectedValueoftheProbabilityDistribution

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Therandomvariablexrepresentsthenumberofboysinafamilyofthreechildren.Assumingthatboysand

girlsareequallylikely,findthemeanandstandarddeviationfortherandomvariablex.

A) mean:1.50;standarddeviation:0.87 B) mean:2.25;standarddeviation:0.87

C) mean:1.50;standarddeviation:0.76 D) mean:2.25;standarddeviation:0.76

2) Therandomvariablexrepresentsthenumberofteststhatapatiententeringahospitalwillhavealongwiththe

correspondingprobabilities.Findthemeanandstandarddeviation.

x01234

P(x) 3

A) mean:1.59;standarddeviation:1.09 B) mean:1.59;standarddeviation:3.71

C) mean:2.52;standarddeviation:1.93 D) mean:3.72;standarddeviation:2.52

3) Therandomvariablexrepresentsthenumberofcreditcardsthatadultshavealongwiththecorresponding

probabilities.Findthemeanandstandarddeviation.

xP(x)

0 0.07

1 0.68

2 0.21

3 0.03

4 0.01

A) mean:1.23;standarddeviation:0.66 B) mean:1.30;standarddeviation:0.32

C) mean:1.30;standarddeviation:0.44 D) mean:1.23;standarddeviation:0.44

Page95

4) Inapizzatakeoutrestaurant,thefollowingprobabilitydistributionwasobtained.Therandomvariablex

representsthenumberoftoppingsforalargepizza.Findthemeanandstandarddeviation.

x P(x)

0 0.30

1 0.40

2 0.20

3 0.06

40.04

A) mean:1.14;standarddeviation:1.04 B) mean:1.54;standarddeviation:1.30

C) mean:1.30;standarddeviation:2.38 D) mean:1.30;standarddeviation:1.54

5) Onethousandticketsaresoldat$2each.Oneticketwillberandomlyselectedandthewinnerwillreceivea

colortelevisionvaluedat$387.Whatistheexpectedvalueforapersonthatbuysoneticket?

A) –$1.61 B) $1.61 C) $1.00 D) –$1.00

6) Ifapersonrollsdoubleswhentossingtwodice,therollerprofits$100.Ifthegameisfair,howmuchshouldthe

personpaytoplaythegame?

A) $20 B) $100 C) $99 D) $97

7) Ataraffle,10,000ticketsaresoldat$5eachforthreeprizesvaluedat$4,800,$1,200,and$400.Whatisthe

expectedvalueofoneticket?

A) –$4.36 B) $4.36 C) $0.64 D) –$0.64

8) Ataraffle,10,000ticketsaresoldat$10eachforthreeprizesvaluedat$4,800,$1,200,and$400.Whatisthe

expectedvalueofoneticket?

A) –$9.36 B) $9.36 C) –$0.64 D) $0.64

9) Inaraffle,1,000ticketsaresoldfor$2each.Oneticketwillberandomlyselectedandthewinnerwillreceivea

laptopcomputervaluedat$1200.Whatistheexpectedvalueforapersonthatbuysoneticket?

A) –$0.80 B) $0.8 C) $1.20 D) –$1.20

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

10) Fromtheprobabilitydistribution,findthemeanandstandarddeviationfortherandomvariablex,which

representsthenumberofcarsperhouseholdinatownof1000households.

xP(x)

00.125

1 0.428

2 0.256

3 0.108

4 0.083

4.2 BinomialDistributions

1 DetermineifanExperimentisaBinomialExperiment

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Youobservethegenderof

thenext250babiesbornatalocalhospital.Therandomvariablerepresentsthenumberofgirls.

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2) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Yourolladie100 times.The

randomvariablerepresentsthenumberthatappearsoneachrollofthedie.

3) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Youspinanumberwheel

thathas19numbers450times.Therandomvariablerepresentsthewinningnumbersoneachspinofthe

wheel.

4) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Youtestfourpainrelievers.

Therandomvariablerepresentsthepainrelieverthatismosteffective.

5) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Testingapainrelieverusing

740peopletodetermineifitiseffective.Therandomvariablerepresentsthenumberofpeoplewhofindthe

painrelievertobeeffective.

6) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Surveying250 prisonersto

seehowmanycrimesinwhichtheywereconvicted.Therandomvariablerepresentsthenumberofcrimesin

whicheachprisonerwasconvicted.

7) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Surveying600 prisonersto

seewhethertheyareservingtimefortheirfirstoffense.Therandomvariablerepresentsthenumberof

prisonersservingtimefortheirfirstoffense.

8) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Eachweek,amanplaysa

gameinwhichhehasa39%chanceofwinning.Therandomvariableisthenumberoftimeshewinsin51

weeks.

9) Decidewhethertheexperimentisabinomialexperiment.Ifitisnot,explainwhy.Selectingfivecards,oneata

timewithoutreplacement,fromastandarddeckofcards.Therandomvariableisthenumberofredcards

obtained.

2 FindtheMean,Variance,andStandardDeviationofaBinomialDistribution

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Findthemeanofthebinomialdistributionforwhichn=40 andp=0.2.

A) 8 B) 2.53 C) 20 D) 40

2) Findthevarianceofthebinomialdistributionforwhichn=800 andp=0.87.

A) 90.48 B) 9.51 C) 696 D) 32.54

3) Findthestandarddeviationofthebinomialdistributionforwhichn=1000 andp=0.94.

A) 7.51 B) 56.4 C) 940 D) 6.31

4) Atestconsistsof700trueorfalsequestions.Ifthestudentguessesoneachquestion,whatisthemeannumber

ofcorrectanswers?

A) 350 B) 0 C) 700 D) 140

5) Atestconsistsof800trueorfalsequestions.Ifthestudentguessesoneachquestion,whatisthestandard

deviationofthenumberofcorrectanswers?

A) 14.14 B) 0 C) 2 D) 20

6) Inarecentsurvey,80%ofthecommunityfavoredbuildingapolicesubstationintheirneighborhood.If15

citizensarechosen,whatisthemeannumberfavoringthesubstation?

A) 12 B) 15 C) 8 D) 10

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7) Inarecentsurvey,80%ofthecommunityfavoredbuildingapolicesubstationintheirneighborhood.If15

citizensarechosen,whatisthestandarddeviationofthenumberfavoringthesubstation?

A) 1.55 B) 2.40 C) 0.98 D) 0.55

8) Theprobabilitythatahouseinanurbanareawillbeburglarizedis5%.If20housesarerandomlyselected,

whatisthemeanofthenumberofhousesburglarized?

A) 1 B) 10 C) 0.5 D) 1.5

9) Inonecity,24%ofadultssmoke.Ingroupsofsize130 ofadults,whatisthevarianceofthenumberthatsmoke

A) 23.71 B) 4.87 C) 31.2 D) 11.86

10) Atestconsistsof100multiplechoicequestions,eachwithfivepossibleanswers,onlyoneofwhichiscorrect.

Findthemeanandthestandarddeviationofthenumberofcorrectanswers.

A) mean:20;standarddeviation:4 B) mean:20;standarddeviation:4.47

C) mean:50;standarddeviation:4 D) mean:50;standarddeviation:7.07

11) Theprobabilitythatanindividualisleft–handedis0.16.Inaclassof10 students,whatisthemeanand

standarddeviationofthenumberofleft–handersintheclass?

A) mean:1.6;standarddeviation:1.16 B) mean:10;standarddeviation:1.16

C) mean:1.6;standarddeviation:1.26 D) mean:10;standarddeviation:1.26

12) Arecentsurveyfoundthat63%ofalladultsover50wearglassesfordriving.Inarandomsampleof100 adults

over50,whatisthemeanandstandarddeviationofthosethatwearglasses?

A) mean:63;standarddeviation:4.83 B) mean:63;standarddeviation:7.94

C) mean:37;standarddeviation:4.83 D) mean:37;standarddeviation:7.94

13) Accordingtogovernmentdata,theprobabilitythatawomanbetweentheagesof25and29wasnevermarried

is40%.Inarandomsurveyof10womeninthisagegroup,whatisthemeanandstandarddeviationofthe

numberthatnevermarried?

A) mean:4;standarddeviation:1.55 B) mean:6;standarddeviation:1.55

C) mean:6;standarddeviation:155 D) mean:4;standarddeviation:2.4

14) Accordingtopolicesources,acarwithacertainprotectionsystemwillberecovered90%ofthetime.If600

stolencarsarerandomlyselected,whatisthemeanandstandarddeviationofthenumberofcarsrecovered

afterbeingstolen?

A) mean:540;standarddeviation:7.35 B) mean:540;standarddeviation:54

C) mean:306:standarddeviation:7.35 D) mean:306:standarddeviation:54

15) Theprobabilitythatatennissetwillgotoatiebreakeris16%.In220 randomlyselectedtennissets,whatisthe

meanandthestandarddeviationofthenumberoftiebreakers?

A) mean:35.2;standarddeviation:5.44 B) mean:35.2;standarddeviation:5.93

C) mean:33;standarddeviation:5.44 D) mean:33;standarddeviation:5.93

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

16) Assumethatmaleandfemalebirthsareequallylikelyandthatthebirthofanychilddoesnotaffectthe

probabilityofthegenderofanyotherchildren.Supposethat500coupleseachhaveababy;findthemeanand

standarddeviationforthenumberofgirlsinthe500babies.

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3 FindBinomialProbabilities

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Assumethatmaleandfemalebirthsareequallylikelyandthatthebirthofanychilddoesnotaffectthe

probabilityofthegenderofanyotherchildren.Findtheprobabilityofexactlynineboysintenbirths.

A) 0.010 B) 0.9 C) 0.020 D) 0.09

2) Assumethatmaleandfemalebirthsareequallylikelyandthatthebirthofanychilddoesnotaffectthe

probabilityofthegenderofanyotherchildren.Findtheprobabilityofatmostthreeboysintenbirths.

A) 0.172 B) 0.300 C) 0.003 D) 0.333

3) Atestconsistsof10trueorfalsequestions.Topassthetestastudentmustansweratleasteightquestions

correctly.Ifthestudentguessesoneachquestion,whatistheprobabilitythatthestudentwillpassthetest?

A) 0.055 B) 0.8 C) 0.20 D) 0.08

4) Atestconsistsof10multiplechoicequestions,eachwithfivepossibleanswers,oneofwhichiscorrect.Topass

thetestastudentmustget60%orbetteronthetest.Ifastudentrandomlyguesses,whatistheprobabilitythat

thestudentwillpassthetest?

A) 0.006 B) 0.060 C) 0.377 D) 0.205

5) Inarecentsurvey,64%ofthecommunityfavoredbuildingapolicesubstationintheirneighborhood.If14

citizensarechosen,findtheprobabilitythatexactly8ofthemfavorthebuildingofthepolicesubstation.

A) 0.184 B) 0.058 C) 0.571 D) 0.640

6) Theprobabilitythatanindividualisleft–handedis0.12.Inaclassof39 students,whatistheprobabilityof

findingfiveleft–handers?

A) 0.186 B) 0.128 C) 0.000 D) 0.12

7) Arecentsurveyfoundthat70%ofalladultsover50wearglassesfordriving.Inarandomsampleof10adults

over50,whatistheprobabilitythatatleastsixwearglasses?

A) 0.850 B) 0.700 C) 0.200 D) 0.006

8) Accordingtogovernmentdata,theprobabilitythatawomanbetweentheagesof25and29wasnevermarried

is40%.Inarandomsurveyof10womeninthisagegroup,whatistheprobabilitythattwoorfewerwerenever

married?

A) 0.167 B) 1.002 C) 0.013 D) 0.161

9) Accordingtogovernmentdata,theprobabilitythatawomanbetweentheagesof25and29wasnevermarried

is40%.Inarandomsurveyof10womeninthisagegroup,whatistheprobabilitythatatleasteightwere

married?

A) 0.167 B) 1.002 C) 0.013 D) 0.161

10) Accordingtopolicesources,acarwithacertainprotectionsystemwillberecovered89%ofthetime.Findthe

probabilitythat3of7stolencarswillberecovered.

A) 0.004 B) 0.429 C) 0.89 D) 0.11

11) Theprobabilitythatatennissetwillgotoatie–

reakeris14%.Whatistheprobabilitythattwoofthreesets

willgototie–breakers?

A) 0.051 B) 0.14 C) 0.311 D) 0.0196

12) Fiftypercentofthepeoplethatgetmail–ordercatalogsordersomething.Findtheprobabilitythatexactly two

of10peoplegettingthesecatalogswillordersomething.

A) 0.044 B) 0.200 C) 0.001 D) 11.250

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13) Theprobabilitythatahouseinanurbanareawillbeburglarizedis5%.If82 housesarerandomlyselected,

whatistheprobabilitythatnoneofthehouseswillbeburglarized?

A) 0.015 B) 0.050 C) 0.000 D) 0.001

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

14) Anairlinehasapolicyofbookingasmanyas150personsonaplanethatseats140.Paststudiesindicatethat

only85%ofbookedpassengersshowupfortheirflight.Findtheprobabilitythatiftheairlinebooks150

personsfora140–seatplane,notenoughseatswillbeavailable.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

15) Sixty–fivepercentofmenconsiderthemselvesknowledgeablefootballfans.If10menarerandomlyselected,

findtheprobabilitythatexactlysixofthemwillconsiderthemselvesknowledgeablefans.

A) 0.238 B) 0.069 C) 0.65 D) 0.600

4 ConstructBinomialDistributions

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Youobservethegenderofthenext100babiesbornatalocalhospital.Youcountthenumberofgirlsborn.

Identifythevaluesofn,p,andq,andlistthepossiblevaluesoftherandomvariablex.

2) Twenty–sixpercentofpeopleintheUnitedStateswithInternetaccessgoonlinetogetnews.Arandom

sampleoffiveAmericanswithInternetaccessisselectedandaskediftheygetthenewsonline.Identifythe

valuesofn,p,andq,andlistthepossiblevaluesoftherandomvariablex.

3) Fifty–sevenpercentoffamiliessaythattheirchildrenhaveaninfluenceontheirvacationplans.Considera

sampleofeightfamilieswhoareaskediftheirchildreninfluencetheirvacationplans.Identifythevaluesofn,

p,andq,andlistthepossiblevaluesoftherandomvariablex.

4) Thirty–eightpercentofpeopleintheUnitedStateshavetypeO+blood.Yourandomlyselect30Americans

andaskthemiftheirbloodtypeisO+.Identifythevaluesofn,p,andq,andlistthepossiblevaluesofthe

randomvariablex.

5) Seventypercentofadultsages50andolderwanttoreachtheir100thbirthday.Yourandomlyselectnineadults

ages50andolderandaskthemwhethertheywanttoreachtheir100thbirthday.Therandomvariable

representsthenumberofadultsages50andolderwhowanttoreachtheir100thbirthday.Graphthebinomial

distributionusingahistogramanddescribeitsshape.

6) ThirtypercentofvotersthinkthatCongressshouldhelpwritestandardsforschoolfood.Yourandomlyselect

eightvotersandaskthemwhetherCongressshouldhelpwritestandardsforschoolfood.Therandomvariable

representsthenumberofvoterswhothinkthatCongressshouldhelpwritestandardsforschoolfood.Graph

thebinomialdistributionusingahistogramanddescribeitsshape.

4.3 MoreDiscreteProbabilityDistributions

1 FindProbabilitiesUsingtheGeometricDistribution

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Acompanyshipscomputercomponentsinboxesthatcontain90 items.Assumethattheprobabilityofa

defectivecomputercomponentis0.21.Findtheprobabilitythatthefirstdefectisfoundintheseventh

componenttested.Roundyouranswertofourdecimalplaces.

Page100

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

2) BasketballplayerChaunceyBillupsoftheDetroitPistonsmakesfreethrowshots88%ofthetime.Findthe

probabilitythathemisseshisfirstshotandmakesthesecond.

A) 0.1056 B) 0.7744 C) 0.0144 D) 0.50

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

3) Acompanyshipscomputercomponentsinboxesthatcontain10 items.Assumethattheprobabilityofa

defectivecomputercomponentis0.1.Usethegeometricmeantofindthemeannumberofdefectiveparts.

Interprettheresults.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

4) Acompanyshipscomputercomponentsinboxesthatcontain10 items.Assumethattheprobabilityofa

defectivecomputercomponentis0.1.Usethegeometricvariancetofindthevarianceofdefectiveparts.

A) 90 B) 0.12345679 C) 0 D) 8100

2 FindProbabilitiesUsingthePoissonDistribution

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Astatisticsprofessorfindsthatwhenheschedulesanofficehouratthe10:30a.m.timeslot,anaverageofthree

studentsarrive.UsethePoissondistributiontofindtheprobabilitythatinarandomlyselectedofficehourin

the10:30a.m.timeslotexactlytwostudentswillarrive.

A) 0.2241 B) 0.6091 C) 0.1992 D) 0.5415

2) Astatisticsprofessorfindsthatwhenheschedulesanofficehouratthe10:30a.m.timeslot,anaverageofthree

studentsarrives.UsethePoissondistributiontofindtheprobabilitythatinarandomlyselectedofficehourno

studentswillarrive.

A) 0.0498 B) 0.1225 C) 0.1108 D) 0.0743

3) Asalesfirmreceivesanaverageoffourcallsperhouronitstoll–freenumber.Foranygivenhour,findthe

probabilitythatitwillreceiveexactlyninecalls.UsethePoissondistribution.

A) 0.0132 B) 0.0001 C) 146.3700 D) 0.0003

4) Asalesfirmreceivesanaverageofthreecallsperhouronitstoll–freenumber.Foranygivenhour,findthe

probabilitythatitwillreceiveatleastthreecalls.UsethePoissondistribution.

A) 0.5768 B) 0.1891 C) 0.4232 D) 0.6138

5) Amail–ordercompanyreceivesanaverageoffiveordersper500solicitations.Ifitsendsout100

advertisements,findtheprobabilityofreceivingatleasttwoorders.UsethePoissondistribution.

A) 0.2642 B) 0.1839 C) 0.9048 D) 0.9596

6) Alocalfirestationreceivesanaverageof0.55rescuecallsperday.UsethePoissondistributiontofindthe

probabilitythatonarandomlyselectedday,thefirestationwillreceivefewerthantwocalls.

A) 0.894 B) 0.106 C) 0.317 D) 0.087

7) Acartowingservicecompanyaveragestwocallsperhour.UsethePoissondistributiontodeterminethe

probabilitythatinarandomlyselectedhourthenumberofcallsissix.

A) 0.0120 B) 0.0002 C) 0.0068 D) 0.0001

8) Abookcontains500pages.Ifthereare200typingerrorsrandomlydistributedthroughoutthebook,usethe

Poissondistributiontodeterminetheprobabilitythatapagecontainsexactlytwoerrors.

A) 0.0536 B) 0.0108 C) 0.4423 D) 0.0893

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3 DecideiftheProbabilityDistributionisBinomial,Geometric,orPoisson

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Decidewhichprobabilitydistribution–binomial,geometric,orPoisson–appliestothequestion.Youdonotneedto

answerthequestion.

1) Given:Theprobabilitythatafederalincometaxreturnisfilledoutincorrectlywithanerrorinfavorofthe

taxpayeris20%.Question:Whatistheprobabilitythatofthetentaxreturnsrandomlyselectedforanaudit,

threereturnswillcontainonlyerrorsfavoringthetaxpayer?

inomial B) geometric C) Poisson

2) Given:Theprobabilitythatafederalincometaxreturnisfilledoutincorrectlywithanerrorinfavorofthe

taxpayeris20%.Question:Whatistheprobabilitythatofthetentaxreturnsrandomlyselectedforanauditin

agivenweek,threereturnswillcontainonlyerrorsfavoringthetaxpayer?

A) Poisson B) geometric C)

inomial

3) Given:Theprobabilitythatafederalincometaxreturnisfilledoutincorrectlywithanerrorinfavorofthe

taxpayeris20%.Question:Whatistheprobabilitythatwhenthetentaxreturnsarerandomlyselectedforan

audit,thesixthreturnwillcontainonlyerrorsfavoringthetaxpayer?

A) geometric B)

inomial C) Poisson

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Ch.4 DiscreteProbabilityDistributions

AnswerKey

4.1 ProbabilityDistributions

1 DecideifaRandomVariableisDiscreteorContinuous

2 FindProbabilities

3ConstructProbabilityDistributions

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Page104

Page105

4 DetermineifaDistributionisaProbabilityDistribution

5FindtheExpectedValueoftheProbabilityDistribution

4.2 BinomialDistributions

1 DetermineifanExperimentisaBinomialExperiment

Page106

2 FindtheMean,Variance,andStandardDeviationofaBinomialDistribution

Page107

4.3 MoreDiscreteProbabilityDistributions

1 FindProbabilitiesUsingtheGeometricDistribution

2 FindProbabilitiesUsingthePoissonDistribution

Page108

3 DecideiftheProbabilityDistributionisBinomial,Geometric,orPoisson

Page109