# On a standard measure of hearing ability the mean is 300 and the standard deviation is 20. What is the raw score for people whose z scores on this test are -4.5?

May 15, 2018

The raw score for people whose z scores on this test are -4.5 $= 210$

#### Explanation:

$z = \frac{x - \overline{x}}{\sigma}$

$- 4.5 = \frac{x - 300}{20}$

$\frac{x - 300}{20} = - 4.5$

$x - 300 = - 4.5 \times 20 = - 90$

$x = - 90 + 300 = 210$

$x = 210$

The raw score for people whose z scores on this test are -4.5 $= 210$