Question

One of the tallest living men has a height of 236 cm. One of the tallest living women is 224 cm tall. Heights of men have a mean of 170 cm and a standard deviation of 6 cm. Heights of women have a mean of 161 cm and a standard deviation of 5 cm. Relative to the population of the same​ gender, who is​ taller? Explain. Choose the correct answer below.

A. The woman is relatively taller because the z score for her height is greater than the z score for the man​'s height.
B. The man is relatively taller because the z score for his height is less than the z score for the woman​'s height.
C. The man is relatively taller because the z score for his height is greater than the z score for the woman​'s height.
D. The woman is relatively taller because the z score for her height is less than the z score for the man​'s height.

Answer 1

A. The woman is relatively taller because the z score for her height is greater than the z score for the man​'s height.

Explanation:

Whoever has the highest z-score, is taller relative to the population of the same gender.

The z-score of a value X in a set with mean
`\mu` and standard deviation
`/sigma` is given by:

`Z = (X - \mu)/(\sigma)`

Solution:

Heights of men have a mean of 170 cm and a standard deviation of 6 cm. One of the tallest living men has a height of 236 cm. So the z-score of his height is:

`Z = (X - \mu)/(\sigma) = (236-170)/(6) = 11`

Heights of women have a mean of 161 cm and a standard deviation of 5 cm.

One of the tallest living women is 224 cm tall. The z-score of the women's height is

`Z = (X - \mu)/(\sigma) = (224-161)/(5) = 12.6`

The women has a higher z-score, so she is relatively taller.

The correct answer is A