Question

According to the United States Health and Human Services, the mean height for Americans is 1.757 meters for men and 1.618 meters for women. The standard deviation is 0.074 meters for men's height and 0.069 meters for women's height. Michelle’s height is 1.758 meters. What is her z-score?

Answer 1

Answer:

Her z-score is 2.03.

Step-by-step explanation:

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

Michelle’s height is 1.758 meters. What is her z-score?

Michelle's is a woman.

The average height of women is $\mu = 1.618$ and the standard deviation is $\sigma = 0.069$

This is Z when X = 1.758. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1.758 - 1.618}{0.069}$

$Z = 2.03$

Her z-score is 2.03.