商务统计学（英文版第7版）教学课件BSFC7e_CH06.ppt

TheNormalDistributionChapter6

ObjectivesInthischapter,youlearn:TocomputeprobabilitiesfromthenormaldistributionHowtousethenormaldistributiontosolvebusinessproblemsTousethenormalprobabilityplottodeterminewhetherasetofdataisapproximatelynormallydistributed

ContinuousProbabilityDistributionsAcontinuousvariableisavariablethatcanassumeanyvalueonacontinuum(canassumeanuncountablenumberofvalues)thicknessofanitemtimerequiredtocompleteatasktemperatureofasolutionheight,ininchesThesecanpotentiallytakeonanyvaluedependingonlyontheabilitytopreciselyandaccuratelymeasure

TheNormalDistribution‘BellShaped’SymmetricalMean,MedianandMode areEqualLocationisdeterminedbythemean,μSpreadisdeterminedbythestandarddeviation,σTherandomvariablehasaninfinitetheoreticalrange:+?to??Mean=Median=ModeXf(X)μσ

TheNormalDistribution

DensityFunctionTheformulaforthenormalprobabilitydensityfunctionisWhere e=themathematicalconstantapproximatedby2.71828 π=themathematicalconstantapproximatedby3.14159 μ=thepopulationmean σ=thepopulationstandarddeviation X=anyvalueofthecontinuousvariable

Byvaryingtheparametersμandσ,weobtaindifferentnormaldistributionsABCAandBhavethesamemeanbutdifferentstandarddeviations.BandChavedifferentmeansanddifferentstandarddeviations.

TheNormalDistributionShapeXf(X)μσChangingμshiftsthedistributionleftorright.Changingσincreasesordecreasesthespread.

TheStandardizedNormalAnynormaldistribution(withanymeanandstandarddeviationcombination)canbetransformedintothestandardizednormaldistribution(Z)TocomputenormalprobabilitiesneedtotransformXunitsintoZunitsThestandardizednormaldistribution(Z)hasameanof0andastandarddeviationof1

TranslationtotheStandardizedNormalDistributionTranslatefromXtothestandardizednormal(the“Z”