1 Ashley is enrolled in an introductory programming class an

1. Ashley is enrolled in an introductory programming class and a communications class at the university. She took an exam in her programming class and got a score of 76; the class mean was 64 and the standard deviation was 8. Ashley also took an exam in her communications class and got a score of 72; the class mean was 60 and the standard deviation was 7.5. Answer the following questions assuming that the distributions of tests scores are normal.

A) Find Ashley’s z-scores in her programming class and in her communications class. __________________________________________________________________________________

B) Explain in which class she performed better relative to her classmates. __________________________________________________________________________________ __________________________________________________________________________________

Solution

Mean ( u ) =64
Standard Deviation ( sd )=8
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
programming class = P(X = 76) = (76-64)/8
= 12/8= 1.5

commmunication class = P(X = 72) = (72-60)/7.5
= 12/7.5= 1.6

b)
Programming
P(X < 76) = (76-64)/8
= 12/8= 1.5
= P ( Z <1.5) From Standard Normal Table
= 0.9332  
Commmunication
P(X < 72) = (72-60)/7.5
= 12/7.5= 1.6
= P ( Z <1.6) From Standard Normal Table
= 0.9452                  

In Commmunication she performed well as the reason she scores better percentile in it