Question

a set of data items is normally distributed with a mean of 80 and a standard deviation of 6. convert 74 to a z - score.

$z_{74}=\square$
(do not round until the final answer. then round to the nearest hundredth as needed.)

Explanation:

Step1: Recall z - score formula

The formula for 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, $x = 74$, $\mu=80$, and $\sigma = 6$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{74 - 80}{6}$.

Step4: Calculate numerator and denominator

First, calculate the numerator: $74-80=-6$. Then divide by the denominator: $\frac{-6}{6}=-1$.

Answer:

-1