Question

A researcher finds that the mean value of depression = 15, and the variance = 9. Which Depression Score corresponds to a z-score of +1?

Answer 1

Given :-

Mean ($\mu$) = 15

Variance ($\sigma^2$) = 9

standard deviation. ($\sigma$) = $\sqrt(\sigma^2)$ = $\sqrt(9)$ = 3

Let, z-score is z=1

Therefore,

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

=> x = $\mu$ + (z*$\sigma$)

=> x = 15 + (1*3)

x = 18

Answer :- Depression score is 18.