Question

a set of data items is normally distributed with a mean of 40 and a standard deviation of 6. convert 40 to a z - score.
$z_{40}=0$
(do not round until the final answer. then round to the nearest hundredth as needed.)

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Substitute values

Given $\mu = 40$, $\sigma=6$, and $x = 40$. Substitute into the formula: $z=\frac{40 - 40}{6}$.

Step3: Calculate the z - score

$\frac{40 - 40}{6}=\frac{0}{6}=0$.

Answer:

$0$