At one university, the students are given z-scores at the end of each semester instead of traditional GPA's. The mean and standard deviation of all the student' culmulative GPA's, on which the z-scores are based, are 2.7 and .5 respectively.

Question

i understand how to translate the pas given the z-scores; however, i don't understand this question:

the president of the university wishes to graduate the top 16% of students with cum laude honors and the top 2.5% with summa cum laude honors. where should the limits be set in terms of z-scores [approx]? in terms of GPAs? what assumption if any did you make about the distribution of the GPAs at the university?

am i supposed to assume that there's a normal distribution? i don't understand how to get the answers to this question.
thank you.

Answer 1

oh wait...should use the 97.5 percentile to get the answer to the 2.5% top students?? because they wouldn't have negative z-scores, right?

Answer 2

Yes, assume a normal distribution.
100 - 2.5 = 97.5%
so any F(z) > .975 gets Summa
My table of z versus F(z) is pretty crude.
for example it has entries
z = 1.9 when F(z) = .971
z = 2.0 when F(z) = .977
We know that somewhere between z = 1.9 and z = 2.0, F (z) = .975
Say maybe any z over 1.95 gets summa.
Now do the same thing for F(z) = 1-.16 = .84
find z for f(z) = .84 (z around 1.0)
any z between there and 1.95 gets cum laude

Answer 3

Yes