GPAs of students. At one university, the students are given z-scores at the end of 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 .5, respectively.

a. Translate each of the following z-scores to corresponding GPA scores: z = 2.0, z = -1.0, z = .5, z = -2.5.

b. Students with z-scores below -1.6 are put on probation.

What is the corresponding probationary GPA?

c. The president of the university wishes to graduate the top 16% of the students with cum laude honors and the top 2.5% with summa cum laude honors. Where (approximately)

should the limits be set in terms of z-scores? In terms of GPAs? What assumption, if any, did you make about the distribution of the GPAs at the university?