Question

a value that is two standard deviations below the mean will be a z - score of \boxed{}.

Explanation:

Step1: Recall z - score formula

The formula for 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: Analyze the position relative to mean

If a value is two standard deviations below the mean, then $x=\mu - 2\sigma$. Substitute this into the z - score formula: $z=\frac{(\mu - 2\sigma)-\mu}{\sigma}=\frac{- 2\sigma}{\sigma}=- 2$.

Answer:

-2