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Chapter05-DiscreteProbabilityDistributions
CopyrightCengageLearning.PoweredbyCognero.
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PAGE
1.
Whichofthefollowingisacharacteristicofanexperimentwherethebinomialprobabilitydistributionisapplicable?
a.
Theexperimenthasatleasttwopossibleoutcomes
b.
Exactlytwooutcomesarepossibleoneachtrial
c.
Thetrialsaredependentoneachother
d.
Theprobabilitiesoftheoutcomeschangesfromonetrial
ANSWER:
b
2.
Anumericaldescriptionoftheoutcomeofanexperimentiscalleda
a.
descriptivestatistic.
b.
probabilityfunction.
c.
variance.
d.
randomvariable.
ANSWER:
d
3.
Aprobabilitydistributionshowingtheprobabilityofxsuccessesinntrials,wheretheprobabilityofsuccessdoesnotchangefromtrialtotrial,istermeda
a.
uniformprobabilitydistribution.
b.
binomialprobabilitydistribution.
c.
hypergeometricprobabilitydistribution.
d.
normalprobabilitydistribution.
ANSWER:
b
4.
Acontinuousrandomvariablemayassume
a.
anynumerical
valueinanintervalorcollectionofintervals.
b.
finitenumberofvaluesinacollectionofintervals.
c.
aninfinitesequenceofvalues.
d.
onlythepositiveintegervaluesinaninterval.
ANSWER:
a
5.
Adescriptionofthedistributionofthevaluesofarandomvariableandtheirassociatedprobabilitiesiscalleda
a.
probabilitydistribution.
b.
empiricaldiscretedistribution.
c.
bivariatedistribution.
d.
tableofbinomialprobability.
ANSWER:
a
6.
Whichofthefollowingisarequiredconditionforadiscreteprobabilityfunction?
a.
∑f(x)=0forallvaluesofx
b.
f(x)1forallvaluesofx
c.
f(x)<0forallvaluesofx
d.
∑f(x)=1forallvaluesofx
ANSWER:
d
7.
Ameasureoftheaveragevalueofarandomvariableiscalleda(n)
a.
variance.
b.
standarddeviation.
c.
expectedvalue.
d.
coefficientofvariation.
ANSWER:
c
8.
Whichofthefollowingis
arequiredconditionforadiscreteprobabilityfunction?
a.
f(x)
0forallvaluesofx
b.
∑f(x)=1forallvaluesofx
c.
∑f(x)=0forallvaluesofx
d.
∑f(x)1forallvaluesofx
ANSWER:
b
9.
Aweightedaverageofthevaluesofarandomvariable,wheretheprobabilityfunctionprovidesweights,isknownasthe
a.
probablevalue.
b.
medianvalue.
c.
expectedvalue.
d.
variance.
ANSWER:
c
10.
Anexperimentconsistsofdeterminingthespeedofautomobilesonahighwaybytheuseofradarequipment.Therandomvariableinthisexperimentisa_____randomvariable.
a.
discrete
b.
continuous
c.
mixedtype
d.
multivariate
ANSWER:
b
11.
Thenumberofcustomersthatenterastoreduringonedayisanexampleof
a.
acontinuousrandomvariable.
b.
adiscreterandomvariable.
c.
eitheracontinuousoradiscreterandomvariable,dependingon
whetheroddorevennumberofthecustomersenter.
d.
eitheracontinuousoradiscreterandomvariable,dependingonthegenderofthecustomers.
ANSWER:
b
12.
Theweightofanobjectisanexampleof
a.
acontinuousrandomvariable.
b.
adiscreterandomvariable.
c.
eitheracontinuousoradiscreterandomvariable,dependingonthe
natureoftheobject.
d.
eitheracontinuousoradiscreterandomvariable,dependingontheunitofmeasurement.
ANSWER:
a
13.
Threepercentofthecustomersofamortgagecompanydefaultontheirpayments.Asampleoffivecustomersisselected.Whatistheprobabilitythatexactlytwocustomersinthesamplewilldefaultontheirpayments?
a.
0.0003
b.
0.0082
c.
0.0077
d.
0.0008
ANSWER:
b
14.
Twentypercentofthestudentsinaclassof400areplanningtogotograduateschool.Thestandarddeviationofthisbinomialdistributionis
a.
20.
b.
64.
c.
8.
d.
40.
ANSWER:
c
15.
Inthetextileindustry,amanufacturerisinterestedinthenumberofblemishesorflawsoccurringineach100feetofmaterial.Theprobabilitydistributionthathasthegreatestchanceofapplyingtothissituationisthe_____distribution
a.
Normal
b.
Binomial
c.
Poisson
d.
Uniform
ANSWER:
c
16.
ThePoissonprobabilitydistributionisa_____probabilitydistribution.
a.
continuous
b.
discrete
c.
uniform
d.
normal
ANSWER:
b
17.
Thebinomialprobabilitydistributionisusedwitha(n)_____randomvariable.
a.
continuous
b.
discrete
c.
uniform
d.
intermittent
ANSWER:
b
18.
Theexpectedvalueofadiscreterandomvariable
a.
isthemostlikelyorhighestprobabilityvaluefortherandomvariable.
b.
willalwaysbeoneofthevaluesxcantakeon,althoughitmaynotbethehighestprobabilityvaluefortherandomvariable.
c.
istheaveragevaluefortherandomvariableovermanyrepeatsoftheexperiment.
d.
isthevalueitisexpectedtoassumeinthenexttrial.
ANSWER:
c
19.
Whichofthefollowingisnotacharacteristicofanexperimentwherethebinomialprobabilitydistributionisapplicable?
a.
Theexperimenthasasequenceofnidenticaltrials.
b.
Exactlytwooutcomesarepossibleoneachtrial.
c.
Thetrialsaredependent.
d.
Theprobabilitiesoftheoutcomesdonotchangefromonetrialtoanother.
ANSWER:
c
20.
Theexpectedvalueofarandomvariableis
a.
thevalueoftherandomvariablethatshouldbeobservedonthenextrepeatoftheexperiment.
b.
thevalueoftherandomvariablethatoccursmostfrequently.
c.
thesquarerootofthevariance.
d.
Noneofthesealternativesiscorrect.
ANSWER:
d
21.
Whichofthefollowingisnotapropertyofabinomialexperiment?
a.
Theexperimentconsistsofasequenceofnidenticaltrials.
b.
Eachoutcomecanbereferredtoasasuccessorafailure.
c.
Theprobabilitiesofthetwooutcomescanchangefromonetrialtothenext.
d.
Thetrialsareindependent.
ANSWER:
c
22.
Inabinomialexperiment,theprobability
a.
doesnotchangefromtrialtotrial.
b.
changesfromtrialtotrial.
c.
couldchangefromtrialtotrial,dependingonthesituationunderconsideration.
d.
couldchangedependingonthenumberofoutcomes.
ANSWER:
a
23.
ThePoissonprobabilitydistributionisusedwith_____randomvariable.
a.
acontinuous
b.
adiscrete
c.
eitheracontinuousordiscrete
d.
any
ANSWER:
b
24.
ThevarianceVar(x)forthebinomialdistributionisgivenbyequation
a.
np(n-1).
b.
np(1-np).
c.
n(1-p).
d.
np(1-p).
ANSWER:
d
25.
Theexpectedvalueforabinomialdistributionisgivenbyequation
a.
(n-1)(1-p).
b.
n(1-p).
c.
np.
d.
(n-1)p.
ANSWER:
c
26.
Aproductionprocessproduces2.5%defectiveparts.Asampleoffivepartsfromtheproductionprocessisselected.Whatistheprobabilitythatthesamplecontainsexactlytwodefectiveparts?
a.
0.2637
b.
0.0058
c.
0.0000
d.
0.0250
ANSWER:
b
27.
Whendealingwiththenumberofoccurrencesofaneventoveraspecifiedintervaloftimeorspace,theappropriateprobabilitydistributionisa_____
distribution.
a.
Binomial
b.
Poisson
c.
Normal
d.
Hypergeometricprobability
ANSWER:
b
28.
Thekeydifferencebetweenthebinomialandhypergeometricdistributionisthat,withthehypergeometricdistributionthe
a.
probabilityofsuccessmustbelessthan0.5.
b.
probabilityofsuccesschangesfromtrialtotrial.
c.
trialsareindependentofeachother.
d.
randomvariableiscontinuous.
ANSWER:
b
29.
Assumethatyouhaveabinomialexperimentwithp=0.4andasamplesizeof150.Thevarianceofthisdistributionis
a.
36.
b.
6.
c.
2.9.
d.
216.
ANSWER:
a
30.
Inabinomialexperimenttheprobabilityofsuccessis0.05.Whatistheprobabilityoftwosuccessesinseventrials?
a.
0.0036
b.
0.0000
c.
0.0406
d.
0.3667
ANSWER:
c
31.
Randomvariablexhastheprobabilityfunctionf(x)=X/6,
forx=1,2or3?
Theexpectedvalueofxis
a.
0.333.
b.
0.500.
c.
2.000.
d.
2.333.
ANSWER:
d
32.
Arandomvariablethatmaytakeonanyvalueinanintervalorcollectionofintervalsisknownasa_____randomvariable.
a.
continuous
b.
discrete
c.
mixedtype
d.
multivariate
ANSWER:
a
33.
Thefollowingrepresentstheprobabilitydistributionforthedailydemandofcomputersatalocalstore.
Demand
Probability
0
0.15
1
0.25
2
0.35
3
0.2
4
0.05
?
Theexpecteddailydemandis
a.
1.0.
b.
1.75.
c.
2.0.
d.
1.09.
ANSWER:
b
34.
Thefollowingrepresentstheprobabilitydistributionforthedailydemandofcomputersatalocalstore.
Demand
Probability
0
0.15
1
0.25
2
0.35
3
0.20
4
0.05
?
Theprobabilityofhavingademandforatleasttwocomputersis
a.
0.75.
b.
0.35.
c.
0.60.
d.
1.00.
ANSWER:
c
35.
Thestudentbodyofalargeuniversityconsistsof60%femalestudents.
Arandomsampleof8studentsisselected.
Whatistheprobabilitythatamongthestudentsinthesampleexactlytwoaremale?
a.
0.0896
b.
0.2090
c.
0.0413
d.
0.0007
ANSWER:
c
36.
Thestudentbodyofalargeuniversityconsistsof60%femalestudents.
Arandomsampleof8studentsisselected.
Whatistheprobabilitythatamongthestudentsinthesampleatleast6arefemale?
a.
0.3154
b.
0.6846
c.
0.0168
d.
0.8936
ANSWER:
a
37.
Thestudentbodyofalargeuniversityconsistsof65%femalestudents.
Arandomsampleof8studentsisselected.
Whatistheprobabilitythatamongthestudentsinthesampleatleast6aremale?
a.
0.0036
b.
0.1691
c.
0.4278
d.
0.0253
ANSWER:
d
38.
Rothisacomputer-consultingfirm.Thenumberofnewclientsthattheyhaveobtainedeachmonthhasrangedfrom0to6.Thenumberofnewclientshastheprobabilitydistributionthatisshownbelow.
Numberof
NewClients
Probability
0
0.05
1
0.10
2
0.15
3
0.30
4
0.25
5
0.10
6
0.05
?
Theexpectednumberofnewclientspermonthis
a.
6.
b.
0.
c.
3.1.
d.
3.
ANSWER:
c
39.
Rothisacomputer-consultingfirm.Thenumberofnewclientsthattheyhaveobtainedeachmonthhasrangedfrom0to6.Thenumberofnewclientshastheprobabilitydistributionthatisshownbelow.
Numberof
NewClients
Probability
0
0.05
1
0.10
2
0.15
3
0.30
4
0.25
5
0.10
6
0.05
?
Thevarianceis
a.
1.45.
b.
2.09.
c.
3.1.
d.
9.61.
ANSWER:
b
40.
Rothisacomputer-consultingfirm.Thenumberofnewclientsthattheyhaveobtainedeachmonthhasrangedfrom0to6.Thenumberofnewclientshastheprobabilitydistributionthatisshownbelow.
?
Numberof
NewClients
Probability
0
0.05
1
0.10
2
0.15
3
0.30
4
0.25
5
0.10
6
0.05
?
Thestandarddeviationis
a.
1.45.
b.
2.09.
c.
3.1.
d.
9.61.
ANSWER:
a
41.
Forty-fourpercentofallregisteredvotersinanationalelectionarefemale.
Arandomsampleof5votersisselected.
Theprobabilitythatthesamplecontains2femalevotersis
a.
0.6600.
b.
0.6114.
c.
0.5000.
d.
0.3400.
ANSWER:
d
42.
Forty-fourpercentofallregisteredvotersinanationalelectionarefemale.Arandomsampleof5votersisselected.
Theprobabilitythattherearenofemalesinthesampleis
a.
0.0551.
b.
0.9450.
c.
0.4400.
d.
0.1649.
ANSWER:
a
43.
Considertheprobabilitydistributionbelow.
x
f(x)
10
.2
20
.4
30
.3
40
.1
?
Theexpectedvalueofxequals
a.
23.
b.
25.
c.
30.
d.
100.
ANSWER:
a
44.
Considertheprobabilitydistributionbelow.
x
f(x)
10
.2
20
.4
30
.3
40
.1
?
Thevarianceofxequals
a.
9.
b.
23.
c.
81.
d.
610.
ANSWER:
c
45.
Asampleof2,500peoplewasaskedhowmanycupsofcoffeetheydrinkinthemorning.Youaregiventhefollowingsampleinformation.
CupsofCoffee
Frequency
0
700
1
900
2
500
3
400
2,500
?
Theexpectednumberofcupsofcoffeeis
a.
1.
b.
1.24.
c.
1.5.
d.
1.03.
ANSWER:
b
46.
Asampleof2,500peoplewasaskedhowmanycupsofcoffeetheydrinkinthemorning.Youaregiventhefollowingsampleinformation.
CupsofCoffee
Frequency
0
700
1
900
2
500
3
400
2,500
?
Thevarianceofthenumberofcupsofcoffeeis
a.
1.06.
b.
1.03.
c.
2.25.
d.
1.24.
ANSWER:
a
47.
TheprobabilitythatPetewillcatchfishwhenhegoesfishingis.88.Peteisgoingtofish3daysnextweek.DefinetherandomvariablextobethenumberofdaysPetecatchesfish.TheprobabilitythatPetewillcatchfishonexactlyonedayis
a.
0.880.
b.
0.038.
c.
0.040.
d.
0.960.
ANSWER:
b
48.
TheprobabilitythatPetewillcatchfishwhenhegoesfishingis.88.Peteisgoingtofish3daysnextweek.DefinetherandomvariablextobethenumberofdaysPetecatchesfish.TheprobabilitythatPetewillcatchfishononedayorlessis
a.
0.880.
b.
0.038.
c.
0.040.
d.
0.960.
ANSWER:
c
49.
TheprobabilitythatPetewillcatchfishwhenhegoesfishingis.88.Peteisgoingtofish3daysnextweek.DefinetherandomvariablextobethenumberofdaysPetecatchesfish.TheexpectednumberofdaysPetewillcatchfishis
a.
0.56.
b.
0.88.
c.
2.64.
d.
0.3168.
ANSWER:
c
50.
TheprobabilitythatPetewillcatchfishwhenhegoesfishingis.88.Peteisgoingtofish3daysnextweek.DefinetherandomvariablextobethenumberofdaysPetecatchesfish.ThevarianceofthenumberofdaysPetewillcatchfishis
a.
0.56.
b.
0.88.
c.
2.64.
d.
0.3168.
ANSWER:
d
51.
Therandomvariablexisthenumberofoccurrencesofaneventoveranintervaloftenminutes.Itcanbeassumedthattheprobabilityofanoccurrenceisthesameinanytwo-timeperiodsofanequallength.Itisknownthatthemeannumberofoccurrencesintenminutesis5.3.Whichofthefollowingdiscreteprobabilitydistributions'propertiesaresatisfiedbyrandomvariablex?
a.
Normal
b.
Poisson
c.
Binomial
d.
Hypergeometric
ANSWER:
b
52.
Therandomvariablexisthenumberofoccurrencesofaneventoveranintervaloftenminutes.Itcanbeassumedthattheprobabilityofanoccurrenceisthesameinanytwotimeperiodsofanequallength.Itisknownthatthemeannumberofoccurrencesintenminutesis5.3.Theappropriateprobabilitydistributionfortherandomvariableis
a.
discrete.
b.
continuous.
c.
eitherdiscreteorcontinuousdependingonhowtheintervalisdefined.
d.
binomial.
ANSWER:
a
53.
Therandomvariablexisthenumberofoccurrencesofaneventoveranintervaloftenminutes.Itcanbeassumedthattheprobabilityofanoccurrenceisthesameinanytwotimeperiodsofanequallength.Itisknownthatthemeannumberofoccurrencesintenminutesis5.3.Theexpectedvalueoftherandomvariablexis
a.
2.
b.
5.3.
c.
10.
d.
2.30.
ANSWER:
b
54.
Therandomvariablexisthenumberofoccurrencesofaneventoveranintervaloftenminutes.Itcanbeassumedthattheprobabilityofanoccurrenceisthesameinanytwotimeperiodsofanequallength.Itisknownthatthemeannumberofoccurrencesintenminutesis5.3.Theprobabilitythatthereare8occurrencesintenminutesis
a.
.0241.
b.
.0771.
c.
.1126.
d.
.9107.
ANSWER:
b
55.
Therandomvariablexisthenumberofoccurrencesofaneventoveranintervaloftenminutes.Itcanbeassumedthattheprobabilityofanoccurrenceisthesameinanytwotimeperiodsofanequallength.Itisknownthatthemeannumberofoccurrencesintenminutesis5.3.Theprobabilitythattherearelessthan3occurrencesis
a.
.0659.
b.
.0948.
c.
.1016.
d.
.1239.
ANSWER:
c
56.
TheprobabilitydistributionforthedailysalesatMichael'sCo.isgivenbelow.
DailySales
(In$1,000s)
Probability
40
0.1
50
0.4
60
0.3
70
0.2
?
Theprobabilityofhavingsalesofnomorethan$60,000is
a.
0.7.
b.
0.2.
c.
0.8.
d.
0.5.
ANSWER:
c
57.
TheprobabilitydistributionforthedailysalesatMichael'sCo.isgivenbelow.
DailySales
(In$1,000s)
Probability
40
0.1
50
0.4
60
0.3
70
0.2
?
Theprobabilityofhavingsalesofatleast$50,000is
a.
0.5
b.
0.10.
c.
0.30.
d.
0.90.
ANSWER:
d
58.
TheprobabilitydistributionforthenumberofgoalstheLionssoccerteammakespergameisgivenbelow.
Number
OfGoals
Probability
0
0.05
1
0.15
2
0.35
3
0.30
4
0.15
?
WhatistheprobabilitythatinagivengametheLionswillscoreatleast1goal?
a.
0.20.
b.
0.55.
c.
1.0.
d.
0.95.
ANSWER:
d
59.
OrientalReproductions,Inc.isacompanythatproduceshandmadecarpetswithorientaldesigns.Theproductionrecordsshowthatthemonthlyproductionhasrangedfrom1to5carpets.Theproductionlevelsandtheirrespectiveprobabilitiesareshownbelow.
Production
PerMonth
Probability
1
0.01
2
0.04
3
0.10
4
0.80
5
0.05
Theexpectedmonthlyproductionlevelis
a.
1.00.
b.
4.00.
c.
3.00.
d.
3.84.
ANSWER:
d
60.
OrientalReproductions,Inc.isacompanythatproduceshandmadecarpetswithorientaldesigns.
Theproductionrecordsshowthatthemonthlyproductionhasrangedfrom1to5carpets.Theproductionlevelsandtheirrespectiveprobabilitiesareshownbelow.
Production
PerMonth
Probability
1
0.01
2
0.04
3
0.10
4
0.80
5
0.05
Thestandarddeviationfortheproductionis
a.
4.32.
b.
3.74.
c.
0.374.
d.
0.612.
ANSWER:
d
61.
Thirty-sixpercentofthestudentsinamanagementclassaregraduatestudents.Arandomsampleof5studentsisselected.Usingthebinomialprobabilityfunction,determinetheprobabilitythatthesamplecontainsexactly2graduatestudents?(Roundtofourdecimalplaces.)
ANSWER:
0.3397(rounded)
62.
Seventy-fivepercentofthestudentsapplyingtoauniversityareaccepted.Usingthebinomialprobabilitytables,whatistheprobabilitythatamongthenext18applicants
a.
Atleast6willbeaccepted?
b.
Exactly10willbeaccepted?
c.
Exactly8willberejected?
d.
Fifteenormorewillbeaccepted?
e.
Determinetheexpectednumberofacceptances.
f.
Computethestandarddeviation.
?
ANSWER:
?
a.
0.9998
b.
0.0376
c.
0.0042
d.
0.3057
e.
13.5
f.
1.8371
?
63.
GeneralHospitalhasnotedthattheyadmitanaverageof7patientsperhour.
a.
Whatistheprobabilitythatduringthenexthourlessthan3patientswillbeadmitted?
b.
Whatistheprobabilitythatduringthenexttwohoursexactly7patientswillbeadmitted?
ANSWER:
?
a.
0.0296
b.
0.0222
64.
Thedemandforaproductvariesfrommonthtomonth.Basedonthepastyear'sdata,thefollowingprobabilitydistributionshowsMNMcompany'smonthlydemand.
x
f(x)
UnitDemand
Probability
0
0.10
1,000
0.20
2,000
0.25
3,000
0.35
4,000
0.10
?
a.
Determinetheexpectednumberofunitsdemandedpermonth.
b.
Eachunitproducedcoststhecompany$8.00,andissoldfor$10.00.Howmuchwillthecompanygainorloseinamonthiftheystocktheexpectednumberofunitsdemanded,butsell2000units?
ANSWER:
?
a.
2150
b.
Profit=$2800
65.
Thirty-fivepercentofthefishinatankareguppies.Arandomsampleof7fishisselected.
a.
Whatistheprobabilitythatthesamplecontainsexactly4guppies?
b.
Whatistheprobabilitythatthesamplecontainsfewerthan2guppies?
c.
Whatistheprobabilitythatthesamplecontainsexactly1non-guppy?
d.
Whatistheexpectednumberofguppies
inthesample?
e.
Whatisthevarianceoftheguppies?
ANSWER:
?
a.
0.1442
b.
0.2338
c.
0.1848
d.
2.45
e.
1.5925
66.
Asalespersoncontactseightpotentialcustomersperday.Frompastexperience,weknowthattheprobabilityofapotentialcustomermakingapurchaseis.10.
a.
Whatistheprobabilitythatthesalespersonwillmakeatleastexactlytwosalesinaday?
b.
Whatistheprobabilitythatthesalespersonwillmakeatleasttwosalesinaday?
c.
Whatpercentageofdayswillthesalespersonnotmakeasale?
d.
Whatistheexpectednumberofsalesperday?
ANSWER:
a.
0.1488
b.
0.1869
c.
43.05%
d.
0.8
67.
AlifeinsurancecompanyhasdeterminedthateachweekanaverageofsevenclaimsisfiledinitsNashvillebranch.
a.
Whatistheprobabilitythatduringthenextweekexactlysevenclaimswillbefiled?
b.
Whatistheprobabilitythatduringthenextweeknoclaimswillbefiled?
c.
Whatistheprobabilitythatduringthenextweekfewerthanfourclaimswillbefiled?
d.
Whatistheprobabilitythatduringthenextweekatleastseventeenclaimswillbefiled?
ANSWER:
a.
0.1490
b.
0.0009
c.
0.0817
d.
0.0009
68.
Whenaparticularmachineisfunctioningproperly,85%oftheitemsproducedarenon-defective.Ifthreeitemsareexamined,whatistheprobabilitythatoneisdefective?Usethebinomialprobabilityfunctiontoanswerthisquestion.
ANSWER:
0.325
69.
Tenpercentoftheitemsproducedbyamachinearedefective.Outof15itemschosenatrandom,
a.
whatistheprobabilitythatexactly3itemswillbedefective?
b.
whatistheprobabilitythatlessthan3itemswillbedefective?
c.
whatistheprobabilitythatexactly11itemswillbenon-defective?
ANSWER:
a.
0.1285
b.
0.816
c.
0.0428
70.
Thestudentbodyofalargeuniversityconsistsof30%Businessmajors.Arandomsampleof20studentsisselected.
a.
Whatistheprobabilitythatamongthestudentsinthesampleatleast10areBusinessmajors?
b.
Whatistheprobabilitythatatleast16arenotBusinessmajors?
c.
Whatistheprobabilitythatexactly10areBusinessmajors?
d.
Whatistheprobabilitythatexactly12arenotBusinessmajors?
ANSWER:
a.
0.0479
b.
0.2374
c.
0.0308
d.
0.1144
71.
ShoppersenterHamiltonPlaceMallatanaverageof120perhour.
?
a.
Whatistheprobabilitythatexactly5shopperswillenterthemallbetweennoonand12:05p.m.?
b.
Whatistheprobabilitythatatleast35shopperswillenterthemallbetween5:00and5:10p.m.?
?
ANSWER:
a.
0.0378
b.
0.0015
72.
Aproductionprocessproduces90%non-defectiveparts.Asampleof10partsfromtheproductionprocessisselected.
a.
Whatistheprobabilitythatthesamplewillcontain7non-defectiveparts?
b.
Whatistheprobabilitythatthesamplewillcontainatleast4defectiveparts?
c.
Whatistheprobabilitythatthesamplewillcontainlessthan5non-defectiveparts?
d.
Whatistheprobabilitythatthesamplewillcontainnodefectiveparts?
ANSWER:
a.
0.0574
b.
0.0128
c.
0.0001
d.
0.3487
73.
Fifty-fivepercentoftheapplicationsreceivedforaparticularcreditcardareaccepted.Amongthenexttwelveapplications,
a.
whatistheprobabilitythatallwillberejected?
b.
whatistheprobabilitythatallwillbeaccepted?
c.
whatistheprobabilitythatexactly4willbeaccepted?
d.
whatistheprobabilitythatfewerthan3willbeaccepted?
e.
Determinetheexpectednumberandthevarianceoftheacceptedapplications.
ANSWER:
a.
0.0001
b.
0.0008
c.
0.0762
d.
0.0079
e.
6.60;2.9700
74.
Theprobabilitydistributionofthedailydemandforaproductisshownbelow.
Demand
Probability
0
0.05
1
0.10
2
0.15
3
0.30
4
0.25
5
0.10
6
0.05
?
a.
Whatistheexpectednumberofunitsdemandedperday?
b.
Determinethevarianceandthestandarddeviation.
ANSWER:
?
a.
3.1
b.
variance=2.09
std.dev.=1.446
75.
Inalargecorporation,47%oftheemployeesaremale.Arandomsampleoffiveemployeesisselected.UsetheBinomialprobabilitytablestoanswerthefollowingquestions.
a.
Whatistheprobabilitythatthesamplecontainsexactlythreemaleemployees?
b.
Whatistheprobabilitythatthesamplecontainsnomaleemployees?
c.
Whatistheprobabilitythatthesamplecontainsmorethanthreefemaleemployees?
d.
Whatistheexpectednumberoffemaleemployeesinthesample?
ANSWER:
?
a.
0.2916
b.
0.0412
c.
0.3289
d.
2.65
76.
Forthefollowingprobabilitydistribution:
x
f(x)
0
0.01
1
0.02
2
0.10
3
0.35
4
0.20
5
0.11
6
0.08
7
0.05
8
0.04
9
0.03
10
0.01
?
a.
DetermineE(x).
b.
Determinethevarianceandthestandarddeviation.
ANSWER:
a.
4.14
b.
variance=3.7
std.dev.=1.924
77.
Arandomvariablexhasthefollowingprobabilitydistribution:
x
f(x)
0
0.08
1
0.27
2
0.35
3
0.25
4
0.05
?
a.
Determinetheexpectedvalueofx.
b.
Determinethevariance.
ANSWER:
?
a.
1.92
b.
1.0336
78.
Acompanysellsitsproductstowholesalersinbatchesof1,000unitsonly.Thedailydemandforitsproductandtherespectiveprobabilitiesaregivenbelow.
Demand(Units)
Probability
0
0.2
1000
0.2
2000
0.3
3000
0.2
4000
0.1
?
a.
Determinetheexpecteddailydemand.
b.
Assumethatthecompanysellsitsproductat$3.75perunit.Whatistheexpecteddailyrevenue?
ANSWER:
a.
1800
b.
$6,750
79.
Therecordsofadepartmentstoreshowthat20%ofitscustomerswhomakeapurchase,returnthemerchandiseinordertoexchangeit.Inthenextsixpurchases,
a.
whatistheprobabilitythatthreecustomerswillreturnthemerchandiseforexchange?
b.
whatistheprobabilitythatfourcustomerswillreturnthemerchandiseforexchange?
c.
whatistheprobabilitythatnoneofthecustomerswillreturnthemerchandiseforexchange?
ANSWER:
a.
0.0819
b.
0.0154
c.
0.2621
80.
Inalargeuniversity,55%ofthestudentsarefemale.Ifarandomsampleoftwentystudentsisselected,
a.
whatistheprobabilitythatthesamplecontainsexactlyfourfemalestudents?
b.
whatistheprobabilitythatthesamplewillcontainexactly17femalestudents?
c.
whatistheprobabilitythatthesamplewillcontainexactlytwentyfemalestudents?
d.
whatistheprobabilitythatthesamplewillcontainmorethanninefemalestudents?
e.
whatistheprobabilitythatthesamplewillcontainfewerthanfivefemalestudents?
f.
whatistheexpectednumberoffemalestudents?
ANSWER:
?
a.
0.0013
b.
0.0040
c.
0.0000
d.
0.7507
e.
0.0015
f.
11
81.
Inasouthernstate,itwasrevealedthat5%ofallautomobilesinthestatedidnotpassinspection.Ofthenexttenautomobilesenteringtheinspectionstation,
a.
whatistheprobabilitythatnonewillpassinspection?
b.
whatistheprobabilitythatallwillpassinspection?
c.
whatistheprobabilitythatexactly
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