Question

The mean score on a college placement exam is 550 with a standard deviation of 150. If the scores vary normally, 90% of the test takers score above which score?

Question 3 options:

	358
	742
	886
	336

Answer 1

Solution: The correct option is 358

Explanation:

We are given:

$\boldsymbol{\mu=550,\sigma=150}$

We have to find the score above which lies 90% of scores. In other words, we have to find the score below which lies 10% of scores, Therefore, we first need to find the critical value corresponding to area = 0.10. Using the standard normal table, we have:

$\boldsymbol{z(0.10)=-1.28}$

We can use the z -score formula. The formula is:

$z=\frac{X-\mu}{\sigma}$

$-1.28=\frac{X-550}{150}$

$-1.28 \times 150=X-550$

$-192=X-550$

$X=550-192$

$\boldsymbol{X=358}$

Therefore, 90% of the test takers above 358 score.