There are two colleges within the same city. College ‘A’ grades students on a 4.0 scale and college ‘B’ grades students on a 5.0 scale. John graduated from college ‘A’ with a GPA of 3.6000 / 4.000 and Mary graduated from college ‘B’ with a GPA of 4.000 / 5.000. This year, the mean GPA for graduates of college ‘A’ was 3.5 with a standard deviation of 0.75; the mean GPA for graduates of college ‘B’ was 3.8 with a standard deviation of 0.85. Assuming that both colleges are equally ranked, draw students from the same population, and have similar admissions standards, which student, John or Mary, graduated higher in his/her class?

Assuming that the GPA for both colleges is normally distributed, we can find out which student ranked higher within their respective class by finding the z-score for each student. The student with the highest z-score is at the highest percentile of the distribution and, therefore, has graduated higher in his/her class.

Z-score for John at college A:

Mean = 3.5

Standard Deviation = 0.75

X = 3.6

[tex]z=\frac{X-\mu}{\sigma} =\frac{3.6-3.5}{0.75}\\z= 0.1333[/tex]

Z-score for Mary at college B:

Mean = 3.8

Standard Deviation = 0.85

X = 4.0

[tex]z=\frac{X-\mu}{\sigma} =\frac{4.0-3.8}{0.85}\\z= 0.2353[/tex]

Since Mary has a higher z-score, she graduated higher in her class than John did in his class.