At one university

At one university

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 2.8 and 0.5, respectively. Complete parts a through c.

Translate each of the following z-scores to corresponding GPA scores: z= 2.0, z = −1.0,
z = 0.5, 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? 
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