Download Section 6-3 - Gordon State College

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.
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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:
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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.
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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:
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