Question

A data set is normally distributed with a mean of 52 and a standard deviation of 3.2.

Which is closest z-score for 45?

Answer 1

`z = -2.1875`

Explanation:

The z score is given by the formula

`z = (x - \mu)/(\sigma)`

where

`z =` standard score

`x` = data point = 45 for this problem

`\mu` = mean = 52 for this problem

`\sigma =` standard deviation = 3.2 for this problem

Therefore

`z = (45 - 52)/(3.2) = -2.1875`