Chapter 6, Problem 13E

To determine

To explain whether Julie did better in exam.

Answer to Problem 13E

Julie did better in both exams.

Explanation of Solution

Given:

First exam:

Mean = $\mu$ = 65

Standard deviation = $\sigma$ =10

Second exam:

Mean = $\mu$ = 80

Standard deviation = $\sigma$ =5

Derrick’s scores:

  $x_1$ = $x_2$ = 80

Julie’s scores:

  $x_1$ = 70

  $x_2$ = 90

Formula:

  $z=\frac{x-\mu }{\sigma }$

The z-score of Derrick’s in first exam is,

  $z=\frac{80-65}{10}=1.5$

The z-score of Derrick’s in second exam is,

  $z=\frac{80-80}{5}=0$

The z-score of Julie’s in first exam is,

  $z=\frac{70-65}{10}=0.5$

The z-score of Julie’s in second exam is,

  $z=\frac{90-80}{5}=2$

Higher z-scores for both exams seems to be in the favor of Julie. Therefore, Julie did better in both exams.