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 = ˆ’1.0,z = 0.5, z= ˆ’2.5.b. Students with z-scores below ˆ’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?