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

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 %