Question

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According to a health statistics center, the mean weight of a 20-to-29-year-old female is 156.5 pounds, with a standard
deviation of 51.2 pounds. The mean weight of
a 20-to-29-year-old male is 183.4 pounds, with a standard deviation of 40.0 pounds Who is relatively heavier a 20-to-29-year-old female who weighs 160 pounds or
a 20-to-29-year-old male who weighs 185 pounds?



The Z-score for the female is ?
The Z-score for the male is ?
Thus, the ____ is relatively heavier.
(Round to two decimal places as needed.)

Answer 1

Using z-scores, we find that:

• The z-score for the female is 0.07.
• The z-score for the male is 0.04.
• Thus, the female is relatively heavier.

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The z-score of a measure X in a data-set with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• It measures how many standard deviations X is above or below the mean.

For the female, we have that:

• Mean weight of 156.5 pounds, thus $\mu = 156.5$.
• Standard deviation of 51.2 pounds, thus $\sigma = 51.2$
• Weighs 160 pounds, thus $X = 160$, and the z-score is:

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

$Z = \frac{160 - 156.5}{51.2}$

$Z = 0.07$

The z-score for the female is 0.07.

For the male, we have that:

• Mean weight of 183.4 pounds, thus $\mu = 183.4$.
• Standard deviation of 40 pounds, thus $\sigma = 40$
• Weighs 185 pounds, thus $X = 185$, and the z-score is:

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

$Z = \frac{185 - 183.4}{40}$

$Z = 0.04$

The z-score for the male is 0.04.

Due to the higher z-score, the female is relatively heavier.

A similar problem is given at https://brainly.com/question/15169808