Question

In a particular year, the mean score on the ACT test was 17.2 and the standard deviation was 5.4. The mean score on the SAT mathematics test was 495 and the standard deviation was 120. The distributions of both scores were approximately bell-shaped. Round the answers to two decimal places.

Find the z-score for an ACT score of 16.

Answer 1

`X \sim N(17.2,5.4)`

Where
`\mu=495` and
`\sigma=120`

And the best way to solve this problem is using the normal standard distribution and the z score given by:

`z=(x-\mu)/(\sigma)`

And replacing we got:

`z=(16-17.2)/(5.4)= -0.22`

And the answer for this case would be
`z =-0.22`

Explanation:

Let X the random variable that represent the scores for the SAT of a population, and for this case we know the distribution for X is given by:

`X \sim N(17.2,5.4)`

Where
`\mu=495` and
`\sigma=120`

And the best way to solve this problem is using the normal standard distribution and the z score given by:

`z=(x-\mu)/(\sigma)`

And replacing we got:

`z=(16-17.2)/(5.4)= -0.22`

And the answer for this case would be
`z =-0.22`