Question

A normally distributed random variable X has a mean of 120 and a standard deviation of 8. Find the standard deviation normal values of the following scores:

a.200

b.70

c.150

d.300

Answer 1

$$Z=\dfrac{X-\mu}{\sigma}\sim N(0,1)$$

Given $\mu=120, \sigma=8$

a.

$$Z=\dfrac{200-120}{8}=10$$

b.

$$Z=\dfrac{70-120}{8}=-6.25$$

c.

$$Z=\dfrac{150-120}{8}=3.75$$

d.

$$Z=\dfrac{300-120}{8}=22.5$$