Question

a set of data items is normally distributed with a mean of 80 and a standard deviation of 8. convert 83 to a z-score.

z_{83} = \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

We are given that $x = 83$, $\mu=80$, and $\sigma = 8$.

Step3: Substitute values into formula

Substitute the values into the formula: $z=\frac{83 - 80}{8}=\frac{3}{8}$.

Step4: Calculate and round

Calculate $\frac{3}{8}=0.375$. Rounding to the nearest hundredth, we get $0.38$.

Answer:

$0.38$