Posted by **Karly** on Saturday, May 23, 2009 at 10:42am.

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.

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.

- Statistics -
**Karly**, Saturday, May 23, 2009 at 11:00am
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?

- Statistics -
**Damon**, Saturday, May 23, 2009 at 11:11am
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

- Statistics -
**Damon**, Saturday, May 23, 2009 at 11:12am
Yes

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