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section7.2notes.notebook January17,2012


http://www.rossmanchance.com/applets/sampledata/sampledata.html


Assumescoresareindependent


Howtocombinenormalrandomvariables:

Thesamerulesformeansandvariancesapply

Afterfindingyournewmeanandstandarddeviationcontinuewiththezscorecalculation

TomandGeorgeareplayingtheclubgolftournament.Theirscoresvaryastheyplaythecourserepeatedly.Tom'sscorevariesaccordingtoN(110,10)andGeorgevariesaccordingtoN(100,8).Iftheyplayindependently,whatistheprobabilitythatTomwillscorehigherthanGeorge?

Solution:FindthedistributionofXY.x-y=

2x - y =

Now we want to find the probability that X < Y or X - Y < 0.

P(X - Y) < 0Since this is normally distributed, find the z-score for our desired outcome.

lower


Ex.ElectronicCircuit

Thedesignofanelectroniccircuitcallsfora100ohmresistoranda250ohmresistorconnectedinseriessothattheirresistancesadd.Thecomponentsusedarenotperfectlyuniform,sothattheactualresistancesvaryindependentlyaccordingtotheNormaldistributions.Theresistanceof100ohmresistorshasmean100ohmsandstandarddeviation2.5ohms,whilethatof250ohmresistorshasmean250ohmsandstandarddeviation2.8ohms.

a)Whatisthedistributionofthetotalresistanceofthetwocomponentsinseries?

b)Whatistheprobabilitythatthetotalresistanceliesbetween345and355ohms?

Attachments

SampleData.mht

Rossman/Chance Applet Collection

Sampling Pennies

SMART Notebook

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