Question

A normal distribution of score has a standard deviation of 10 and a mean of 0. What is the z score of a score that is 20 points above the mean?

Answer 1

Given a Normal Distribution, you know that:

- The Standard Deviation is:

$\sigma=10$

- The Mean is:

$\mu=0$

The formula for calculating the z-score is:

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

Where μ is the Mean and σ is the Standard Deviation.

In this case, the score is 20 points above the mean, therefore;

$X=\mu+20=0+20=20$

Therefore, by substituting values into the formula and evaluating, you get:

$z=\frac{20-0}{10}$$z=\frac{20}{10}$$z=2$

Hence, the answer is:

$z=2$