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section7.2notes.notebook January17,2012
section7.2notes.notebook January17,2012
section7.2notes.notebook January17,2012
http://www.rossmanchance.com/applets/sampledata/sampledata.html
section7.2notes.notebook January17,2012
section7.2notes.notebook January17,2012
section7.2notes.notebook January17,2012
section7.2notes.notebook January17,2012
Assumescoresareindependent
section7.2notes.notebook January17,2012
section7.2notes.notebook January17,2012
section7.2notes.notebook January17,2012
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
section7.2notes.notebook January17,2012
Ex.ElectronicCircuit
Thedesignofanelectroniccircuitcallsfora100ohmresistoranda250ohmresistorconnectedinseriessothattheirresistancesadd.Thecomponentsusedarenotperfectlyuniform,sothattheactualresistancesvaryindependentlyaccordingtotheNormaldistributions.Theresistanceof100ohmresistorshasmean100ohmsandstandarddeviation2.5ohms,whilethatof250ohmresistorshasmean250ohmsandstandarddeviation2.8ohms.
a)Whatisthedistributionofthetotalresistanceofthetwocomponentsinseries?
b)Whatistheprobabilitythatthetotalresistanceliesbetween345and355ohms?
section7.2notes.notebook January17,2012
Attachments
SampleData.mht
Rossman/Chance Applet Collection
Sampling Pennies
SMART Notebook
Page 1: Jan 1-4:16 PMPage 2: Jan 1-4:16 PMPage 3: Jan 1-4:16 PMPage 4: Jan 1-4:16 PMPage 5: Jan 1-4:16 PMPage 6: Jan 13-2:02 PMPage 7: Jan 1-4:16 PMPage 8: Jan 1-4:16 PMPage 9: Jan 1-4:16 PMPage 10: Jan 3-7:52 AMPage 11: Jan 13-1:19 PMPage 12: Jan 13-1:30 PMAttachments Page 1