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σ=populationstandarddeviationPleaseNote:Toaccessthenormalpdffunction,press[2nd][VARS][1]TheTI/willcalculateaspecificx-valueorrawscore associatedwithagivencumulativearea(probability)underthenormalcurve(theinversenormalproblem)NormaldistributionusingTIGiventhepopulationmean, μ=;and,thepopulationstandarddeviation,σ=,find:ProbabilityofxUsethenormalcdffunctionoftheTIcalculatortofindtheareaofashadedregionforthis examplewefindtheareatotheleftofthesyntaxisnormalcdf(lowerbound,upperNormaldistributionInthefollowingsubsections,wewillonlycompute probabilitiesinvolving“≤”UsealargenegativenumberlikeinthesecasesScrolldownandselectinvNorm(whichstandsforinversenormaldistributionNormal distributionusingTIGiventhepopulationmean,μ=;and,thepopulationstandarddeviation,σ=,find:ProbabilityofxProbabilityofxgreaterthanandlessthan; thatisP(<x<)Ifwechoosevaluesoftherandomvariableatrandom,andthesamplemeanisTINormalCDFTIOverviewChooseSTAT,thenCALC,thenVar Stats.Whichcanbeaccessedbypressing[2ND][VARS]NormalDisttiNormaldistributionusingTI@Giventhepopulationmean,μ=;and,thepopulation standarddeviation,σ=,find:ProbabilityofxTINormalCDF&TISteps.First,enterthelowerboundary.AlthoughI’musingaTIhere,theTIstepsareidentical: Exampleproblem:AgroupofstudentstakingendofTheNormalProbabilityDistributionmenufortheTI+isfoundunderDISTR(2ndVARS)PressandDISTR (abovethebutton)IfyouhaveStatWizardsenabled(TIPlusFamilyofGraphingCalculatorsOnly),youwillseeamenupromptingforthevaluesOnaTI,the commandisoptionontheDistrmenuNOTE:AmeanofzeroandastandarddeviationofoneareconsideredtobethedefaultThistutorialexplainshowtousethe followingfunctionsonaTIcalculatortofindnormaldistributionprobabilities:normalpdf(x,μ,σ)returnstheprobabilityassociatedwiththenormalpdfwhere:x= individualvalueWatchthevideoforthestepsFillintheboxesasprompted;theywilllookjustliketheonesontheShadeNormscreenEnterthelower boundary,,andthenpressthecommakeynormalcdf(commandfromtheDISTRmenu.Enteryourdatainalist.Nowentertheimportantnumbersinorder.Enter thevalues,highlight"Paste"andpress[ENTER])Pressthe[WINDOW]keyTheTI/willcalculateaspecificx-valueorrawscoreassociatedwithagiven cumulativearea(probability)underthenormalcurve(theinversenormalproblem)However,sincethenormaldistributioniscontinuous,youcouldreplaceallThe threemajorfunctionsfortheNormalCurveontheTI/PluscalculatorsarelocatedintheDistributionmenuEntertheappropriatelist(eg,L1)andenterItwilllook likeVarStatsLTofindprobablyfromanormaldistributionwhenaskedtofindP(lower