Question

select the correct choices that complete the sentences below.

a) a data value that has a negative z-score is dropdown the mean.
b) a data value that has a positive z-score is dropdown the mean.

Explanation:

Define the z-score formula

$$ z = \frac{x - \mu}{\sigma} $$

Analyze negative z-score

$$ z < 0 \implies \frac{x - \mu}{\sigma} < 0 \implies x - \mu < 0 \implies x < \mu $$

Analyze positive z-score

$$ z > 0 \implies \frac{x - \mu}{\sigma} > 0 \implies x - \mu > 0 \implies x > \mu $$

Answer:

Question a

A data value that has a negative z-score is <blank>less than</blank> the mean.

Question b

A data value that has a positive z-score is <blank>greater than</blank> the mean.