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1、Chapter7:SamplingDistributionsandtheCentralLimitTheorem7.1a.–c.Answersvary.d.Thehistogramexhibitsamoundshape.Thesamplemeanshouldbecloseto3.5=μe.Thestandarddeviationshouldbeclosetoσ/3=1.708/3=.9860.f.Verysimilarpictures.7.2a.P(Y=2)=P(W=6)=p(4,1,1)+p(1,4,1)+p(1,
2、1,4)+p(3,2,1)+p(3,1,2)=p(2,3,1)+p(2,1,3)+p(1,3,2)+p(1,2,3)+p(2,2,2)=10.216b.Answersvary,buttherelativefrequencyshouldbefairlyclose.c.Therelativefrequencyshouldbeevencloserthanwhatwasobservedinpartb.7.3a.Thehistogramshouldbesimilarinshape,butthishistogramhasasm
3、allerspread.b.Answersvary.c.Thenormalcurveshouldapproximatethehistogramfairlywell.7.4a.Thehistogramhasaright–skewedshape.Itappearstofollowp(y)=y/21,y=1,…,6.b.FromtheStatReportwindow,μ=2.667,σ=1.491.c.Answersvary.d.i.Ithasaright–skewedshape.ii.Themeanislarger,b
4、utthestd.dev.issmaller.e.i.samplemean=2.667,samplestd.dev=1.491/12=.4304.ii.Thehistogramiscloselymoundshaped.iii.Verycloseindeed.7.5a.Answersvary.b.Answersvary,butthemeansareprobablynotequal.c.Thesamplemeanvaluesclusteraroundthepopulationmean.d.Thetheoreticals
5、tandarddeviationforthesamplemeanis6.03/5=2.6967.e.Thehistogramhasamoundshape.f.Yes.7.6Thelargerthesamplesize,thesmallerthespreadofthehistogram.Thenormalcurvesapproximatethehistogramsequallywell.7.7a.–b.Answersvary.c.Themeanshouldbeclosetothepopulationvarianced
6、.Thesamplingdistributionisnotmound–shapedforthiscase.e.Thetheoreticaldensityshouldfitwell.f.Yes,becausethechi–squaredensityisright–skewed.227.8a.σ=(6.03)=36.3609.b.Thetwohistogramshavesimilarshapes,butthehistogramgeneratedfromthesmallersamplesizeexhibitsagreat
7、erspread.Themeansaresimilar(andclosetothevaluefoundinparta).Thetheoreticaldensityshouldfitwellinbothcases.c.Thehistogramgeneratedwithn=50exhibitsamoundshape.Here,thetheoreticaldensityischi–squarewithν=50–1=49degreesoffreedom(alargevalue).143144Chapter7:Samplin
8、gDistributionsandtheCentralLimitTheoremInstructor’sSolutionsManual7.9a.P(
9、Y–μ
10、≤.3)=P(–1.2≤Z≤1.2)=.7698.b.P(
11、Y–μ
12、≤.3)=P(–.3n≤Z≤.3n)=1–2P(Z>.3n).Forn=25,36,69,and64,theprobabilitiesa
