Question

The scores on a standardized test are normally distributed with a mean of 95 and standard deviation of 10. What test score is 1.7 standard deviations below the mean?

Answer 1

Answer:

$78$

Explanation:

Here, we want to get the test score that is 1.7 SD below the mean

Mathematically:

$z\text{ = }\frac{x-mean}{SD}$

x is the value we want to calculate

mean = 95

SD = 10

z = -1.7 since it is below the mean value

Thus:

$\begin{gathered} -1.7\text{ = }\frac{x-95}{10} \\ \\ 10(-1.7)\text{ = x - 95} \\ -17\text{ = x-95} \\ x\text{ = 95-17} \\ x\text{ = 78} \end{gathered}$