ApplicationsofNormalDistributions-TaosMunicipal…53应用程序的正常分布，陶斯市…

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1、5.3ApplicationsofNormalDistributionsStatisticsMrs.SpitzFall2008Objectives/AssignmentHowtocomparedatafromtwonormaldistributionsHowtofindprobabilitiesfornormallydistributedvariablesusingatableandusingtechnologyHowtofindaspecificdataentryofanormaldistributiongiventheprob

2、ability.Assignment:pp.217-219#1-16ComparingNormalDistributionsIn5.2,youlearnedhowtotransformanormallydistributedvariable,xtoaz-scoreusingtheequationcontinuedYoualsolearnedtofindareasunderthestandardnormalcurve.Inthissection,youwilllearnhowtoapplythoseskills.Forinstanc

3、e,transformingx-valuestoz-scoresallowsyoutocomparevariablesintwonormaldistributionsasshowninthefollowingexample.Ex.1:ComparingscoresfromtwodistributionsTheGraduateRecordExam(GRE)andtheMillerAnalogyTest(MAT)areteststhatgraduateschoolsusetoevaluateapplicants.GREscoresar

4、enormallydistributedwith=1500and=300,whileMATscoresarenormallydistributedwith=50and=5.Youdecidetotakebothtests.Youscore1875ontheGREanda57ontheMAT.Onwhichtestdidyouscorebetter?ExplainSolution:Youcantransformeachscoretoastandardz-scoretodeterminewhichisbetter.Theare

5、atotheleftofthez-scoreisthepercentile.Theareatotheleftofz=1.25is.8944andtheareatotheleftofz=1.4is.9222.TheMATz-scoreisinthe92ndpercentilewhichisgreaterthantheGREz-score(89thpercentile).SoyouscoredbetterontheMAT.ProbabilityandNormalDistributionsIfarandomvariablexisnorm

6、allydistributed,youcanfindtheprobabilitythatxwillfallinagivenintervalbycalculatingthearaunderthenormalcurveforthegiveninterval.Tofindtheareaunderanynormalcurve,firstconverteachdatavaluetoaz-score.Thenusethestandardnormaldistribution.Forinstance,consideranormalcurvewit

7、h=500and=100,asshownattheupperleft.Thevalueofxonestandarddeviationabovethemeanis+=500+100=600.ProbabilityandNormalDistributionsNowconsiderthestandardnormalcurveshownatthelowerleft.Thevalueofzonestandarddeviationabovethemeanis+=0+1=1.Becauseaz-scoreof1corresponds

8、toanx-valueof600andareasarenotchangedwithatransformationtoastandardnormalcurve,theshadedareasinthegraphareequalEx.2:Findingp