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chap06TIFBSAFC5
CHAPTER6:
THENORMALDISTRIBUTION
1.Initsstandardizedform,thenormaldistribution
a）hasameanof0andastandarddeviationof1.
b）hasameanof1andavarianceof0.
c）hasanareaequalto0.5.
d）cannotbeusedtoapproximatediscreteprobabilitydistributions.
ANSWER:
a
TYPE:
MCDIFFICULTY:
Easy
KEYWORDS:
standardizednormaldistribution,properties
2.Whichofthefollowingaboutthenormaldistributionisnottrue?
a）Theoretically,themean,median,andmodearethesame.
b）About2/3oftheobservationsfallwithin
1standarddeviationfromthemean.
c）Itisadiscreteprobabilitydistribution.
d）Itsparametersarethemean,
andstandarddeviation,
.
ANSWER:
c
TYPE:
MCDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,properties
3.Ifaparticularbatchofdataisapproximatelynormallydistributed,wewouldfindthatapproximately
a）2ofevery3observationswouldfallbetween
1standarddeviationaroundthemean.
b）4ofevery5observationswouldfallbetween
1.28standarddeviationsaroundthemean.
c）19ofevery20observationswouldfallbetween
2standarddeviationsaroundthemean.
d）Alltheabove.
ANSWER:
d
TYPE:
MCDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,properties
4.ForsomepositivevalueofZ,theprobabilitythatastandardnormalvariableisbetween0andZis0.3770.ThevalueofZis
a）0.18
b）0.81
c）1.16
d）1.47
ANSWER:
c
TYPE:
MCDIFFICULTY:
Moderate
KEYWORDS:
standardizednormaldistribution,value
5.ForsomevalueofZ,theprobabilitythatastandardnormalvariableisbelowZis0.2090.ThevalueofZis
a）–0.81
b）–0.31
c）0.31
d）1.96
ANSWER:
a
TYPE:
MCDIFFICULTY:
Moderate
KEYWORDS:
standardizednormaldistribution,value
6.ForsomepositivevalueofZ,theprobabilitythatastandardnormalvariableisbetween0andZis0.3340.ThevalueofZis
a）0.07
b）0.37
c）0.97
d）1.06
ANSWER:
c
TYPE:
MCDIFFICULTY:
Moderate
KEYWORDS:
standardizednormaldistribution,value
7.ForsomepositivevalueofX,theprobabilitythatastandardnormalvariableisbetween0and+2Xis0.1255.ThevalueofXis
a）0.99
b）0.40
c）0.32
d）0.16
ANSWER:
d
TYPE:
MCDIFFICULTY:
Difficult
KEYWORDS:
normaldistribution,value
8.ForsomepositivevalueofX,theprobabilitythatastandardnormalvariableisbetween0and+1.5Xis0.4332.ThevalueofXis
a）0.10
b）0.50
c）1.00
d）1.50
ANSWER:
c
TYPE:
MCDIFFICULTY:
Difficult
KEYWORDS:
normaldistribution,value
9.GiventhatXisanormallydistributedrandomvariablewithameanof50andastandarddeviationof2,findtheprobabilitythatXisbetween47and54.
ANSWER:
0.9104
TYPE:
PRDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
10.Acompanythatsellsannuitiesmustbasetheannualpayoutontheprobabilitydistributionofthelengthoflifeoftheparticipantsintheplan.Supposetheprobabilitydistributionofthelifetimesoftheparticipantsisapproximatelyanormaldistributionwithameanof68yearsandastandarddeviationof3.5years.Whatproportionoftheplanrecipientswouldreceivepaymentsbeyondage75?
ANSWER:
0.0228
TYPE:
PRDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
11.Acompanythatsellsannuitiesmustbasetheannualpayoutontheprobabilitydistributionofthelengthoflifeoftheparticipantsintheplan.Supposetheprobabilitydistributionofthelifetimesoftheparticipantsisapproximatelyanormaldistributionwithameanof68yearsandastandarddeviationof3.5years.Whatproportionoftheplanrecipientsdiebeforetheyreachthestandardretirementageof65?
ANSWER:
0.1957usingExcelor0.1949usingTableE.2
TYPE:
PRDIFFICULTY:
Moderate
KEYWORDS:
normaldistribution,probability
12.Acompanythatsellsannuitiesmustbasetheannualpayoutontheprobabilitydistributionofthelengthoflifeoftheparticipantsintheplan.Supposetheprobabilitydistributionofthelifetimesoftheparticipantsisapproximatelyanormaldistributionwithameanof68yearsandastandarddeviationof3.5years.Findtheageatwhichpaymentshaveceasedforapproximately86%oftheplanparticipants.
ANSWER:
71.78yearsold
TYPE:
PRDIFFICULTY:
Difficult
KEYWORDS:
normaldistribution,value
13.Ifweknowthatthelengthoftimeittakesacollegestudenttofindaparkingspotinthelibraryparkinglotfollowsanormaldistributionwithameanof3.5minutesandastandarddeviationof1minute,findtheprobabilitythatarandomlyselectedcollegestudentwillfindaparkingspotinthelibraryparkinglotinlessthan3minutes.
a）0.3551
b）0.3085
c）0.2674
d）0.1915
ANSWER:
b
TYPE:
MCDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
14.Ifweknowthatthelengthoftimeittakesacollegestudenttofindaparkingspotinthelibraryparkinglotfollowsanormaldistributionwithameanof3.5minutesandastandarddeviationof1minute,findtheprobabilitythatarandomlyselectedcollegestudentwilltakebetween2and4.5minutestofindaparkingspotinthelibraryparkinglot.
a）0.0919
b）0.2255
c）0.4938
d）0.7745
ANSWER:
d
TYPE:
MCDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
15.Ifweknowthatthelengthoftimeittakesacollegestudenttofindaparkingspotinthelibraryparkinglotfollowsanormaldistributionwithameanof3.5minutesandastandarddeviationof1minute,findthepointinthedistributioninwhich75.8%ofthecollegestudentsexceedwhentryingtofindaparkingspotinthelibraryparkinglot.
a）2.8minutes
b）3.2minutes
c）3.4minutes
d）4.2minutes
ANSWER:
a
TYPE:
MCDIFFICULTY:
Moderate
KEYWORDS:
normaldistribution,value
16.Theownerofafishmarketdeterminedthattheaverageweightforacatfishis3.2poundswithastandarddeviationof0.8pound.Assumingtheweightsofcatfisharenormallydistributed,theprobabilitythatarandomlyselectedcatfishwillweighmorethan4.4poundsis_______?
ANSWER:
0.0668
TYPE:
FIDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
17.Theownerofafishmarketdeterminedthattheaverageweightforacatfishis3.2poundswithastandarddeviationof0.8pound.Assumingtheweightsofcatfisharenormallydistributed,theprobabilitythatarandomlyselectedcatfishwillweighbetween3and5poundsis_______?
ANSWER:
0.5865
TYPE:
FIDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
18.Theownerofafishmarketdeterminedthattheaverageweightforacatfishis3.2poundswithastandarddeviationof0.8pound.Acitationcatfishshouldbeoneofthetop2%inweight.Assumingtheweightsofcatfisharenormallydistributed,atwhatweight（inpounds）shouldthecitationdesignationbeestablished?
a）1.56pounds
b）4.84pounds
c）5.20pounds
d）7.36pounds
ANSWER:
b
TYPE:
MCDIFFICULTY:
Moderate
KEYWORDS:
normaldistribution,value
19.Theownerofafishmarketdeterminedthattheaverageweightforacatfishis3.2poundswithastandarddeviationof0.8pound.Assumingtheweightsofcatfisharenormallydistributed,abovewhatweight（inpounds）do89.80%oftheweightsoccur?
ANSWER:
2.184pounds
TYPE:
PRDIFFICULTY:
Moderate
KEYWORDS:
normaldistribution,value
20.Theownerofafishmarketdeterminedthattheaverageweightforacatfishis3.2poundswithastandarddeviationof0.8pound.Assumingtheweightsofcatfisharenormallydistributed,theprobabilitythatarandomlyselectedcatfishwillweighlessthan2.2poundsis_______?
ANSWER:
0.1056
TYPE:
FIDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
21.Afoodprocessorpackagesorangejuiceinsmalljars.Theweightsofthefilledjarsareapproximatelynormallydistributedwithameanof10.5ouncesandastandarddeviationof0.3ounce.Findtheproportionofalljarspackagedbythisprocessthathaveweightsthatfallbelow10.875ounces.
ANSWER:
0.8944
TYPE:
PRDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
22.Afoodprocessorpackagesorangejuiceinsmalljars.Theweightsofthefilledjarsareapproximatelynormallydistributedwithameanof10.5ouncesandastandarddeviationof0.3ounce.Findtheproportionofalljarspackagedbythisprocessthathaveweightsthatfallabove10.95ounces.
ANSWER:
0.0668
TYPE:
PRDIFFICULTY:
Easy
KEYWORDS:
normaldistribution,probability
23.TrueorFalse:
Theprobabilitythatastandardnormalrandomvariable,Z,fallsbetween–1.50and0.81is0.7242.
ANSWER:
True
TYPE:
TFDIFFICULTY:
Easy
KEYWORDS:
standardizednormaldistribution,probability
24.TrueorFalse:
Theprobabilitythatastandardnormalrandomvariable,Z,isbetween1.50and2.10isthesameastheprobabilityZisbetween–2.10and–1.50.
ANSWER:
True
TYPE:
TFDIFFICULTY:
Easy
KEYWORDS:
standardizednormaldistribution,probability
25.TrueorFalse:
Theprobabilitythatastandardnormalrandomvariable,Z,isbelow1.96is0.4750.
ANSWER:
False
TYPE:
TFDIFFICULTY:
Easy
KEYWORDS:
standardizednormaldistribution,probability
26.TrueorFalse:
Theprobabilitythatastandardnormalrandomvariable,Z,isbetween1.00and3.00is0.1574.
ANSWER:
True
TYPE:
TFDIFFICULTY:
Easy
KEYWORDS:
standardizednormaldistribution,probability
27.TrueorFalse:
Theprobabilitythatastandardnormalrandomvariable,Z,fallsbetween–2.00and–0.44is0.6472.
ANSWER:
False
TYPE:
TFDIFFICULTY:
Easy
KEYWORDS:
standardizednormaldistribution,probability
28.TrueorFalse:
Theprobabilitythatastandardnormalrandomvariable,Z,islessthan5.0isapproximately0.
ANSWER:
False
TYPE:
TFDIFFICULTY:
Easy
KEYWORDS:
standardizednormaldistribution,probability
29.TrueorFalse:
Aworkerearns$15perhourataplantandistoldthatonly2.5%ofallworkersmakea
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