Chapter 2.1, Problem 19E

To determine

To calculate the Z score for Gerald and Eleanor and also explain who has the higher scores.

Answer to Problem 19E

Eleanor = 1.8

Gerald = 1.6

Explanation of Solution

Given:

SAT score:

Eleanor score = 680

Mean = 500

Standard deviation = 100

ACT score:

Gerald score = 29

Mean = 21

Standard deviation = 5

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

Standardized score:

  $\begin{array}{l}\text{For Eleanor : }\\ \text{z = }\frac{680-500}{100}\\ \text{z = 1}\text{.8}\end{array}$ $\begin{array}{l}\text{For Gerald : }\\ \text{z = }\frac{29-21}{5}\\ \text{z = 1}\text{.6}\end{array}$

The Z score for Eleanor is higher than the Gerald therefore the score of Eleanor is comparatively larger than the Gerald.