Question

a set of data items is normally distributed with a mean of 30 and a standard deviation of 5. convert 21 to a z-score.
z_{21} = \boxed{}
(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 point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $x = 21$, $\mu=30$, and $\sigma = 5$.

Step3: Substitute values into formula

Substitute the values into the z - score formula: $z=\frac{21 - 30}{5}$.

Step4: Calculate numerator and then the fraction

First, calculate the numerator: $21-30=-9$. Then, divide by the standard deviation: $\frac{-9}{5}=-1.8$.

Answer:

-1.8