统计学入门——正态分布

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1、Copyright©2012PearsonEducation,Inc.publishingasPrenticeHallChap6-1Chap6-1Chapter6TheNormalDistributionBasicBusinessStatistics12thEditionCopyright©2012PearsonEducation,Inc.publishingasPrenticeHallChap6-2Chap6-2LearningObjectivesInthischapter,youlearn:Tocom

2、puteprobabilitiesfromthenormaldistributionHowtousethenormaldistributiontosolvebusinessproblemsTousethenormalprobabilityplottodeterminewhetherasetofdataisapproximatelynormallydistributedCopyright©2012PearsonEducation,Inc.publishingasPrenticeHallChap6-3Chap

3、6-3ContinuousProbabilityDistributionsAcontinuousrandomvariableisavariablethatcanassumeanyvalueonacontinuum(canassumeanuncountablenumberofvalues)thicknessofanitemtimerequiredtocompleteatasktemperatureofasolutionheight,ininchesThesecanpotentiallytakeonanyva

4、luedependingonlyontheabilitytopreciselyandaccuratelymeasureCopyright©2012PearsonEducation,Inc.publishingasPrenticeHallChap6-4Chap6-4TheNormalDistribution‘BellShaped’SymmetricalMean,MedianandModeareEqualLocationisdeterminedbythemean,μSpreadisdeterminedbyth

5、estandarddeviation,σTherandomvariablehasaninfinitetheoreticalrange:+toMean=Median=ModeXf(X)μσCopyright©2012PearsonEducation,Inc.publishingasPrenticeHallChap6-5Chap6-5TheNormalDistributionDensityFunctionTheformulaforthenormalprobabilitydensityfunctioni

6、sWheree=themathematicalconstantapproximatedby2.71828π=themathematicalconstantapproximatedby3.14159μ=thepopulationmeanσ=thepopulationstandarddeviationX=anyvalueofthecontinuousvariableCopyright©2012PearsonEducation,Inc.publishingasPrenticeHallChap6-6Chap6-6

7、Byvaryingtheparametersμandσ,weobtaindifferentnormaldistributionsManyNormalDistributionsCopyright©2012PearsonEducation,Inc.publishingasPrenticeHallChap6-7Chap6-7TheNormalDistributionShapeXf(X)μσChangingμshiftsthedistributionleftorright.Changingσincreasesor

8、decreasesthespread.Copyright©2012PearsonEducation,Inc.publishingasPrenticeHallChap6-8Chap6-8TheStandardizedNormalAnynormaldistribution(withanymeanandstandarddeviationcombination)canbetransformedintothestandardizedno