Question

Two students, Ruth and William, want to find out who has the higher GPA when compared to each of their schools. Ruth hasa GPA of 3.7, and her school has a mean GPA of 3.0 and a standard deviation of 0.4. William has a GPA of 3.75, and hisschool has a mean of 3.2 and a standard deviation of 0.5. Who has the higher GPA when compared to each of their schools?

Answer 1

ANSWER

Ruth, since she has a higher z-score.

EXPLANATION

Given a mean μ and a standard deviation σ, the z-score of a measure x is:

$z=\frac{x-\mu}{\sigma}$

For Ruth, her GPA is x = 3.7. Her school has a mean GPA of 3.0 and a standard deviation of 0.4. The z-score is:

$z=\frac{3.7-3.0}{0.4}=1.75$

For William, his GPA is x = 3.75. His school has a mean GPA of 3.2 and a standard deviation of 0.5. His z-score is:

$z=\frac{3.75-3.2}{0.5}=1.1$

Since Ruth has a higher z-score, her GPA is higher when compared to each of their schools.