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.
- translate each of the following z-scores to corresponding GPA: z=2.0, z=-1.0, z=.5, z =-2.5.
- Students with z-scores below -1.6 are put on probation. What is the corresponding probationary GPA?
- 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-score? In terms of GPAs? What assumption, if any, did you make about the distribution of the GPAs at the university?