Question

Standardized tests: In a particular year, the mean score on the ACT test was 27.5 and the standard deviation was 3.3. The mean score on the SAT mathematics test was 537 and the standard deviation was 117. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places.(a) Find the z-score for an ACT score of 15.(b) Find the z-score for a SAT score of 506.

Answer 1

(a) The z-score is -3.79

(b) The z-score is -0.26

Step-by-step explanation:

The formula for the z-score is:

`\begin{gathered} z=(x-\mu)/(\sigma) \\ x=\text{ the data point we want to know the z-score} \\ \mu=mean \\ \sigma=standard\text{ }deviation \end{gathered}`

In a,

Mean = 27.5

Standard deviation = 3.3

x = 15

`z=(15-27.5)/(3.3)=-(12.5)/(3.3)=-3.79`

In b,

Mean = 537

Standard deviation = 117

x = 506

`z=(506-537)/(117)=-0.26`