Question

In a given normal distribution, the population mean is 80 and the population standard deviation is 2.5. Find the corresponding standard z – score of the following values.

Answer 1

We can find z-score using this formula:

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

where X is observed value, $\mu$ is mean of the sample, $\sigma$ is the standard deviation.

We have: $\mu=80, \sigma=2.5$

So, z-value: $Z=\frac{X-80}{2.5}$

There is no X value in this problem, so you should just substitute X for your value and calculate z-score.

For example, if X=84, z-score is $Z=\frac {84-80}{2.5}=1.6$