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2/3/2017 Section 6-3 Applications of Normal Distributions NONSTANDARD NORMAL DISTRIBUTIONS If 0 or 1 (orboth),wewillconvert valuestostandardscoresusingtheformula thenproceduresforworkingwithallnormal distributionsarethesameasthoseforthe standardnormaldistribution. NOTE:Wewillroundz scoresto2decimal places. FINDING AREAS WITH NONSTANDARD NORMAL DISTRIBUTIONS WITH TABLE A-2 1. Sketchanormalcurve,labelthemeanand thespecific values,thenshade theregion correspondingtothedesiredprobability. 2. Foreachrelevantvalue thatisa boundaryfortheshadedregion,usethe formulatoconvertthevaluetoaz score. 3. RefertoTableA‐2tofindtheareaofthe shadedregion.Thisareaisthedesired probability. 1 2/3/2017 z= x– FINDING AREAS WITH NONSTANDARD NORMAL DISTRIBUTIONS WITH TI-83/84 Tofindtheareabetweentwo values,press 2ndVARS (forDIST)andselect2:normalcdf(. Thenenterthetwo valuesseparatedbyacomma followedbyanothercomma,themean,acomma, andthenthestandarddeviation. Tofindtheareabetween58and80when 63.6 and 2.5,yourcalculatordisplayshouldlook like: normalcdf(58,80,63.6,2.5) FINDING AREAS WITH NONSTANDARD NORMAL DISTRIBUTIONS WITH TI-84 NEW OS Tofindtheareabetweentwo values,press 2ndVARS (forDIST)andselect2:normalcdf(.Then enterthetwo valuesseparatedbyacommafollowed byanothercomma,themean,acomma,andthenthe standarddeviation. Tofindthearea between58and80 when 63.6 and 2.5,your calculatordisplay shouldlooklike: 2 2/3/2017 CAUTIONS • Don’tconfusezscoresandareas.Remember z scoresaredistances alongthehorizontal scale,butareasareregions underthe normalcurve.TableA‐2listz scoresinthe leftcolumnsandacrossthetoprow,butareas arefoundinthebodyofthetable. • Choosethecorrect(right/left)sideofthe graph.Avalueseparatingthetop10%from theotherswillbeontherightsideofthegraph, butavalueseparatingthebottom10%willbe ontheleftsideofthegraph. CAUTIONS (CONCLUDED) • Az scoremustbenegative wheneveritis locatedontheleft halfofthenormal distribution. • Areas (orprobabilities)arepositiveorzero values,buttheyarenevernegative. FINDING VALUES FROM KNOWN AREAS USING TABLE A-2 1. Sketchanormaldistributioncurve,enterthe givenprobabilityorpercentageinthe appropriateregionofthegraph,andidentify value(s)beingsought. 2. UseTableA‐2tofindthez scorecorresponding tothecumulativeleftareaboundedby . 3. Usetheformula,entervaluesfor , ,andthez score,thensolvefor .Notethattheformulacan berewrittenas: · 4. Refertothesketchofthecurvetoverifythatthe solutionmakessenseinthecontextofthegraph andinthecontextoftheproblem. 3 2/3/2017 FINDING VALUES FROM KNOWN AREAS USING TI-83/84 Tofindthevaluecorrespondingtoaknownarea, press2ndVARS (forDIST)andselect 3:invNorm(.Thenenterthetotalareatotheleft ofthevalue,themean,andthestandard deviation. Tofindthevaluecorrespondingto0.3786,a cumulativeareatotheleft,when 10 and 2,yourcalculatordisplayshouldlooklike: invNorm(.3786,10,2) FINDING VALUES FROM KNOWN AREAS USING TI-84 NEW OS Tofindthevaluecorrespondingtoaknownarea,press 2ndVARS (forDIST)andselect3:invNorm(.Then enterthetotalareatotheleftofthevalue,themean, andthestandarddeviation. Tofindthevalue correspondingto0.3786, acumulativeareatothe left,when 10 and 2,yourcalculator displayshouldlooklike: 4