Question

Two students, Anita and Manuel, attend different colleges. At each college, the GPAs are normally distributed. Manuel's GPA is two grade points below his school average, while Anita’s GPA is 0.40 standard deviations above her school average. Is it possible for Manuel to have a higher GPA than Anita? Explain in complete sentences

Answer 1

Let the mean of Anita and Manual colleges here be MA and MM here.

Also the standard deviation of Anita and Manual colleges here be SA and SM

Then, we are given here the scores of Anita and Manuel as:

M = MM - 2 and A = MA + 0.4SA

Let Manuel GPA here be higher than GPA of Anita, then we have here:
M > A

MM - 2 > MA + 0.4SA

MM - MA - 0.4SA > 2

This is possible for example:
For Mean GPA of Manuel college: 4

Mean GPA of Anita's college: 1

Standard deviation of Anita's college: 0.1

Then, 4 - 1 - 0.1 = 2.9 > 2

Therefore the given condition is possible here that Manuel can have a higher GPA than Anita.