Statistics
posted by Karly on .
At one university, the students are given zscores 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 zscores are based, are 2.7 and .5 respectively.
i understand how to translate the pas given the zscores; 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 zscores [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.

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

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 
Yes