Question

An incoming freshman took her college’s placement exams in French and mathematics. In French, she scored 82 and in math 86. The overall results on the French exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a standard deviation of 12.
On which exam did she do better compared with the other freshmen?

Answer 1

Answer:

Math exams

Step-by-step explanation:

We have been given that an incoming freshman took her college’s placement exams in French and mathematics. In French, she scored 82 and in math 86. The overall results on the French exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a standard deviation of 12.

We will use z-score formula to solve our given problem.

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

Let us find z-score for French exams.

$z=\frac{82-72}{8}$

$z=\frac{10}{8}$

$z=1.25$

Let us find z-score for Mathematics exams.

$z=\frac{86-68}{12}$

$z=\frac{18}{12}$

$z=1.5$

Since the z-score of math exams is greater than z-score of French exams, therefore, she performed better on Math exams compared with the other freshmen.