Question

a set of data items is normally distributed with a mean of 80 and a standard deviation of 8. convert 80 to a z-score.

$z_{80} = \square$
(do not round until the final answer. then round to the nearest hundredth as needed.)

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

Here, $x = 80$, $\mu=80$, and $\sigma = 8$.

Step3: Substitute into formula

Substitute the values into the formula: $z=\frac{80 - 80}{8}$.

Step4: Simplify the expression

First, calculate the numerator: $80 - 80=0$. Then, divide by the denominator: $\frac{0}{8}=0$.

Answer:

0