Question

Scores on the ACT college entrance exam follow a bell-shaped distribution with mean $21$ and standard deviation 5. Wayne’s standardized score on the ACT was $-0.6$ What was Wayne’s actual ACT score?

a. $3$

b. $13$

c. 1$6$

d. $18$

e. $24$

Short answer

The correct option is (d)$18$

Step-by-step solution

Given information

Mean $=21$

Standard Deviation $=5$

Standardized score is $=-0.6$

Concept

The formula used:$Z=\frac{x-\mu }{\sigma }$

Calculation

$$\begin{gathered} Z=\frac{x-\mu }{\sigma } \\ Z\times \sigma =x-\mu \\ Z\times \sigma +\mu =x \\ x=\mu +Z\times \sigma \\ =21+(-0.6)\times 5 \\ =21-3x \\ =18 \end{gathered}$$

Hence, the correct option is (d)