MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question

Thanks. Why is Kathy's score considered better-is it because it is a posituve score? What does the Z score represent in this case?  

Expert Solution
Check Mark
Step 1: Comparision of z-scores.

Bobby' Z- score (mu equals 896 comma space sigma equals 174 right parenthesis was

Z=fraction numerator x minus mu over denominator sigma end fraction space equals space fraction numerator 1080 minus 896 over denominator 174 end fraction space equals 1.06

Bobby's score  of 1080 was between 1 and 2 standard deviation above the mean  (mu plus 1.06 sigma space equals 1080 right parenthesis


Kathy's Z-score (mu equals 20.6 comma space sigma equals 5.2) was

Z=fraction numerator 28 minus 20.6 over denominator 5.2 end fraction= 1.42

Kathy's score  of 28 was between 1 and 2 standard deviation above the mean (mu space plus factorial.42 sigma space equals 28)

Since Kathy' score is 1.42 sigma above the mean whereas Bobby' score is only 1.06 sigma above the mean,

hence Kathy' score is considered better than Bobby's score.


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