Question

A normally distributed data set has a mean of 53 and a standard deviation of 2.5. What Z-score corresponds to a data value of 47?

Answer 1

`Z=-2.4`

Explanation:

Just use the formula `Z=(X-mu)/sigma` to get `Z=(47-53)/2.5=-6/2.5=-2.4`.

This tells us that the data value 47 is 2.4 standard deviations below the mean. This makes it a mild outlier.