In 2012 the mean score on the ACT test was 211 and the stand

In 2012, 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 Alexandra scored a 24 on the ACT. Cheryl scored a 600. Which score is higher relative to its population? You must show work to receive credit.

Solution

3.

To calculate which performed better relative to its population, we compare the z scores.

For Alexandra:

z = (x - u) / sigma = (24 - 21.1)/5.2 = 0.557692308   

For Cheryl:

z = ( - u) / sigma = (600 - 514)/117 = 0.735042735

Thus, CHERYL has a higher score relative to her population. [ANSWER, CHERYL]