﻿
311
A. 0.6554
B. 0.3446
C. 0.0142
D. 0.9858
E. 0
Exercise7.7.25
(Solutiononp.324.)
FortheCharterSchoolProblem(Example6)inCentralLimitTheorem:UsingtheCentralLimit
Theorem,calculatethefollowingusingthenormalapproximationtothebinomial.
Ifyoueitherhaveaccesstoanappropriatecalculatororcomputersoftware,trycalculatingthese
probabilitiesusingthetechnology. TryalsousingthesuggestionthatisatthebottomofCentral
LimitTheorem:UsingtheCentralLimitTheoremforﬁndingawebsitethatcalculatesbinomial
probabilities.
Exercise7.7.26
(Solutiononp.324.)
Fourfriends,Janice,Barbara,KathyandRoberta,decidedtocarpooltogethertogettoschool.
Eachdaythedriverwouldbechosenbyrandomlyselectingoneofthefournames.Theycarpool
toschoolfor96days. Usethenormalapproximationtothebinomialtocalculatethefollowing
probabilities.Roundthestandarddeviationto4decimalplaces.
A. FindtheprobabilitythatJaniceisthedriveratmost20days.
B. FindtheprobabilitythatRobertaisthedrivermorethan16days.
Ifyoueitherhaveaccesstoanappropriatecalculatororcomputersoftware,trycalculatingthese
probabilitiesusingthetechnology. TryalsousingthesuggestionthatisatthebottomofCentral
LimitTheorem:UsingtheCentralLimitTheoremforﬁndingawebsitethatcalculatesbinomial
probabilities.
**Exercise24contributedbyRobertaBloom
AvailableforfreeatConnexions<http://cnx.org/content/col10522/1.40>
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312
CHAPTER7. THECENTRALLIMITTHEOREM
7.8Review
8
Thenextthreequestionsrefertothefollowinginformation: Richard’sFurnitureCompanydeliversfur-
niturefrom10A.M.to2P.M.continuouslyanduniformly. Weareinterestedinhowlong(inhours)past
the10A.M.starttimethatindividualswaitfortheirdelivery.
Exercise7.8.1
(Solutiononp.325.)
X
A. U(0,4)
B. U(10,2)
C. Exp(2)
D. N(2,1)
Exercise7.8.2
(Solutiononp.325.)
Theaveragewaittimeis:
A. 1hour
B. 2hour
C. 2.5hour
D. 4hour
Exercise7.8.3
(Solutiononp.325.)
least1
1
2
more hoursis:
A.
1
4
B.
1
2
C.
3
4
D.
3
8
Exercise7.8.4
(Solutiononp.325.)
Given:X~Exp
1
3
.
a. FindP(x>1)
b. Calculatetheminimumvaluefortheupperquartile.
c. FindP
x=
1
3
Exercise7.8.5
(Solutiononp.325.)
A. 4years
B. 4.5years
C. 5years
D. 5.5years
8
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313
Exercise7.8.6
(Solutiononp.325.)
Whichofthefollowingdistributionsisdescribedbythefollowingexample?
Manypeoplecanrunashortdistanceofunder2miles,butasthedistanceincreases,fewerpeople
canrunthatfar.
A. Binomial
B. Uniform
C. Exponential
D. Normal
Exercise7.8.7
(Solutiononp.325.)
Thelengthoftimetobrushone’steethisgenerallythoughttobeexponentiallydistributedwith
ameanof
3
4
minutes.Findtheprobabilitythatarandomlyselectedpersonbrusheshis/herteeth
lessthan
3
4
minutes.
A. 0.5
B.
3
4
C. 0.43
D. 0.63
Exercise7.8.8
(Solutiononp.325.)
Whichdistributionaccuratelydescribesthefollowingsituation?
Thechancethatateenageboyregularlygiveshismotherakissgoodnight(andheshould!!) is
X=thenumberofteenageboysthatregularlygivetheirmotherakissgoodnight
A. B(14,0.20)
B. P(2.8)
C. N(2.8,2.24)
D. Exp
1
0.20
Exercise7.8.9
(Solutiononp.325.)
Whichdistributionaccuratelydescribesthefollowingsituation?
A2008reportontechnologyusestatesthatapproximately20percent ofU.S.householdshave
never sent t an e-mail. . (source: : http://www.webguild.org/2008/05/20-percent-of-americans-
have-never-used-email.php)SupposethatweselectarandomsampleoffourteenU.S.households
.
X=thenumberofhouseholdsina2008sampleof14householdsthathaveneversentanemail
A. B(14,0.20)
B. P(2.8)
C. N(2.8,2.24)
D. Exp
1
0.20
**Exercise9contributedbyRobertaBloom
AvailableforfreeatConnexions<http://cnx.org/content/col10522/1.40>
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314
CHAPTER7. THECENTRALLIMITTHEOREM
7.9Lab1:CentralLimitTheorem(PocketChange)
9
ClassTime:
Names:
7.9.1StudentLearningOutcomes:
 ThestudentwilldemonstrateandcomparepropertiesoftheCentralLimitTheorem.
NOTE
: Thislabworksbestwhensamplingfromseveralclassesandcombiningdata.
7.9.2CollecttheData
1. Countthechangeinyourpocket.(Donotincludebills.)
2. Randomlysurvey30classmates.Recordthevaluesofthechange.
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
Table7.1
3. Constructahistogram.Make5-6intervals.Sketchthegraphusingarulerandpencil.Scaletheaxes.
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315
Figure7.1
4. Calculatethefollowing(n=1;surveyingonepersonatatime):
a.
x=
b. s=
5. Drawasmoothcurvethroughthetopsofthebarsofthehistogram.Use1–2completesentencesto
describethegeneralshapeofthecurve.
7.9.3CollectingAveragesofPairs
thechangeof30classmates,recordtheaveragechangeof30pairs.
1. Randomlysurvey30pairsofclassmates.Recordthevaluesoftheaverageoftheirchange.
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
Table7.2
2. Constructahistogram.Scaletheaxesusingthesamescalingyoudidforthesectiontitled"Collecting
theData".Sketchthegraphusingarulerandapencil.
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316
CHAPTER7. THECENTRALLIMITTHEOREM
Figure7.2
3. Calculatethefollowing(n=2;surveyingtwopeopleatatime):
a.
x=
b. s=
4. Drawasmoothcurvethroughtopsofthebarsofthehistogram. . Use1–2complete e sentencesto
describethegeneralshapeofthecurve.
7.9.4CollectingAveragesofGroupsofFive
changeof30classmates,recordtheaveragechangeof30groupsof5.
1. Randomly y survey 30 groups of 5 classmates.
Record the values s of f the e average of their
change.
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
Table7.3
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317
2. Constructahistogram.Scaletheaxesusingthesamescalingyoudidforthesectiontitled"Collectthe
Data".Sketchthegraphusingarulerandapencil.
Figure7.3
3. Calculatethefollowing(n=5;surveyingﬁvepeopleatatime):
a.
x=
b. s=
4. Drawasmoothcurvethroughtopsofthebarsofthehistogram. . Use1–2complete e sentencesto
describethegeneralshapeofthecurve.
7.9.5DiscussionQuestions
1. Asnchanged,whydidtheshapeofthedistributionofthedatachange?Use1–2completesentences
toexplainwhathappened.
2. Inthesectiontitled"CollecttheData",whatwastheapproximatedistributionofthedata?X
3. Inthesectiontitled"CollectingAveragesofGroupsofFive",whatwastheapproximatedistribution
oftheaverages?
X