Chapter 2.1, Problem 11E

To determine

To find: the standardized scores for both students.

Answer to Problem 11E

The standardized score for E is 180 and the standardized score for G is 150

Explanation of Solution

Given:

E scores 680 on the SAT mathematics test Mean 500

Standard deviation =100 E scores 680 on the SAT mathematics test

G scores 27

Mean =18

Standard deviation =6

Calculation:

The standardized score for Eis obtained below.

  $\begin{array}{l}z(\text{Eleanor})=\frac{x-\mu }{\sigma }\\ =\frac{680-500}{100}\\ =1.80\end{array}$

The standardized score for G is obtained below.

  $\begin{array}{l}z(Gerald)=\frac{x-\mu }{\sigma }\\ =\frac{27-18}{6}\\ =1.50\end{array}$

E's score 680 was 1.80 standard deviation above the mean score whereas G's score 27 was 1.50 standard deviation above the mean score.

Conclusion:

Therefore, the standardized score for Eis 180 and the standardized score for G is 150