Chapter 6, Problem 12E

To determine

To explain in which exam she did better.

Answer to Problem 12E

She did better in Math exam.

Explanation of Solution

Given:

French exam:

Score = $x$ = 82

Mean = $\mu$ = 72

Standard deviation = $\sigma$ =8

Math exam:

Temperature = $x$ = 86

Mean = $\mu$ = 68

Standard deviation = $\sigma$ =12

Formula:

  $z=\frac{x-\mu }{\sigma }$

The z-score for French exam is,

  $z=\frac{82-72}{8}=1.25$

The z-score for Math exam is,

  $z=\frac{86-68}{12}=1.5$

Therefore, she was 1.5 standard deviation above the mean in math. Only 1.25 standard deviation above the mean in French exam. Hence, she did better in Math exam.