Chapter 6, Problem 14E

To determine

To explain whether Sara did better in exam.

Answer to Problem 14E

Sara did better.

Explanation of Solution

Given:

First exam:

Mean = $\mu$ = 80

Standard deviation = $\sigma$ =4

Second exam:

Mean = $\mu$ = 70

Standard deviation = $\sigma$ =15

Reginald’s scores:

  $x_1$ =80

  $x_2$ = 85

Sara’s scores:

  $x_1$ = 88

  $x_2$ = 65

Formula:

  $z=\frac{x-\mu }{\sigma }$

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

  $z=\frac{88-80}{4}=2$

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

  $z=\frac{65-70}{15}=-0.33$

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

  $z=\frac{80-80}{4}=0$

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

  $z=\frac{85-70}{15}=1$

On average, z-score of Sara seems to be better relative to class average than the Reginald’s. Therefore, z-score is higher for Sara’s exam score. Hence, Sara did better.