In a recent year, the mean score on the ACT test was 21.1 and the standard deviation was 5.2. The mean score on the SAT mathematics test was 514 and the standard deviation was 117.

The distributions of both scores were approximately bell-shaped.

a. Find the z-score for an ACT score of 27.

b. Find the z-score for an SAT math score of 650.

c. Which score is higher, relative to its population of scores?

d. Jose’s ACT score had a z-score of 0.75. What was his ACT score?

e. Emma’s SAT score had a z-score of −2.0. What was her SAT score?