Question

At one university, the students are given z-scores at the end of the each semester, rather than the traditional gpas. the mean and standard deviation of all students' cumulative gpas, on which the z-scores are based, are 2.7 and 0.5, respectively

Answer 1

 a) 
2=(x-2.7)/.5 
(2)(.5) = x-2.7 
1=x-2.7 
x=3.7 

-2.5=(x-2.7)/.5 
(-2.5)(.5) = x-2.7 
-1.25 =x-2.7 
x=2.7-1.25 = 1.45 

b) 
95% of the students' score lie within 2 standard deviation of the mean. Therefore, the top 2.5% corresponds to a z value of 2. 
The limits are (2, infinity) --- top 2.5 %