Question

find the z - score for 258 given a mean of 273 and a standard deviation of 5.

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

Here, $x = 258$, $\mu=273$, and $\sigma = 5$.

Step3: Substitute into formula

Substitute the values into the formula: $z=\frac{258 - 273}{5}$.

Step4: Calculate numerator

First, calculate the numerator: $258-273=- 15$.

Step5: Calculate z - score

Then, divide the numerator by the standard deviation: $z=\frac{-15}{5}=-3$.

Answer:

-3