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.
A. Findtheprobabilitythatlessthan100favoracharterschoolforgradesK-5.
B. Findtheprobabilitythat170ormorefavoracharterschoolforgradesK-5.
C. Findtheprobabilitythatnomorethan140favoracharterschoolforgradesK-5.
D. Findtheprobabilitythattherearefewerthan130thatfavoracharterschoolforgradesK-5.
E. Findtheprobabilitythatexactly150favoracharterschoolforgradesK-5.
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.
C. FindtheprobabilitythatBarbaradrivesexactly24ofthose96days.
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.)
Supposethatitisnowpastnoononadeliveryday. Theprobabilitythatapersonmustwaitat
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.)
 40%offull-timestudentstook4yearstograduate
 30%offull-timestudentstook5yearstograduate
 20%offull-timestudentstook6yearstograduate
 10%offull-timestudentstook7yearstograduate
Theexpectedtimeforfull-timestudentstograduateis:
A. 4years
B. 4.5years
C. 5years
D. 5.5years
8
Thiscontentisavailableonlineat<http://cnx.org/content/m16955/1.12/>.
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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
about20%.Fourteenteenageboysarerandomlysurveyed.
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.
9Thiscontentisavailableonlineat<http://cnx.org/content/m16950/1.10/>.
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315
Figure7.1
4. Calculatethefollowing(n=1;surveyingonepersonatatime):
a.
x=
b. s=
5. Drawasmoothcurvethroughthetopsofthebarsofthehistogram.Use1–2completesentencesto
describethegeneralshapeofthecurve.
7.9.3CollectingAveragesofPairs
Repeatsteps1-5(ofthesectionabovetitled"CollecttheData")withoneexception. Insteadofrecording
thechangeof30classmates,recordtheaveragechangeof30pairs.
1. Randomlysurvey30pairsofclassmates.Recordthevaluesoftheaverageoftheirchange.
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
__________
Table7.2
2. Constructahistogram.Scaletheaxesusingthesamescalingyoudidforthesectiontitled"Collecting
theData".Sketchthegraphusingarulerandapencil.
AvailableforfreeatConnexions<http://cnx.org/content/col10522/1.40>
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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
Repeatsteps1–5(ofthe sectiontitled"CollecttheData")withoneexception. . Insteadofrecordingthe
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
AvailableforfreeatConnexions<http://cnx.org/content/col10522/1.40>
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
4. In1–2completesentences,explainanydifferencesinyouranswerstotheprevioustwoquestions.
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318
CHAPTER7. THECENTRALLIMITTHEOREM
7.10Lab2:CentralLimitTheorem(CookieRecipes)
10
ClassTime:
Names:
7.10.1StudentLearningOutcomes:
 ThestudentwilldemonstrateandcomparepropertiesoftheCentralLimitTheorem.
7.10.2Given:
X=lengthoftime(indays)thatacookierecipelastedattheOlmsteadHomestead.(Assumethateachof
thedifferentrecipesmakesthesamequantityofcookies.)
Recipe#
X
Recipe#
X
Recipe#
X
Recipe#
X
1
1
16
2
31
3
46
2
2
5
17
2
32
4
47
2
3
2
18
4
33
5
48
11
4
5
19
6
34
6
49
5
5
6
20
1
35
6
50
5
6
1
21
6
36
1
51
4
7
2
22
5
37
1
52
6
8
6
23
2
38
2
53
5
9
5
24
5
39
1
54
1
10
2
25
1
40
6
55
1
11
5
26
6
41
1
56
2
12
1
27
4
42
6
57
4
13
1
28
1
43
2
58
3
14
3
29
6
44
6
59
6
15
2
30
2
45
2
60
5
Table7.4
Calculatethefollowing:
a. m
x
=
b. s
x
=
10
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319
7.10.3CollecttheData
Usearandomnumbergeneratortorandomlyselect4samplesofsizen5fromthegivenpopulation.
Recordyoursamplesbelow.Then,foreachsample,calculatethemeantothenearesttenth.Recordthemin
thespacesprovided.Recordthesamplemeansfortherestoftheclass.
1. Completethetable:
Sample1
Sample2
Sample3
Sample4
Samplemeansfromothergroups:
Means:
x=
x=
x=
x=
Table7.5
2. Calculatethefollowing:
a.
x=
b. s
x
=
3. Again,usearandomnumbergeneratortorandomlyselect4samplesfromthepopulation.Thistime,
makethesamplesofsizen=10.Recordthesamplesbelow.Asbefore,foreachsample,calculatethe
meantothenearesttenth.Recordtheminthespacesprovided.Recordthesamplemeansfortherest
oftheclass.
Sample1
Sample2
Sample3
Sample4
Samplemeansfromothergroups:
Means:
x=
x=
x=
x=
Table7.6
4. Calculatethefollowing:
a.
x=
b. s
x
=
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320
CHAPTER7. THECENTRALLIMITTHEOREM
5. Fortheoriginalpopulation,constructahistogram.Makeintervalswithbarwidth=1day.Sketchthe
graphusingarulerandpencil.Scaletheaxes.
Figure7.4
6. Drawasmoothcurvethroughthetopsofthebarsofthehistogram.Use1–2completesentencesto
describethegeneralshapeofthecurve.
7.10.4RepeattheProcedureforn=5
1. Forthesampleofn=5daysaveragedtogether,constructahistogramoftheaverages(yourmeans
togetherwiththemeansoftheothergroups). Makeintervalswithbarwidths=
1
2
day. Sketchthe
graphusingarulerandpencil.Scaletheaxes.
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