Question

The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.5 inches. Men the same age have mean height 69 inches with standard deviation 2.8 inches. (a) What is the z-score for a woman who is 6 feet tall? Please use 2 decimal places. (b) What is the z-score for a man who is 6 feet tall? Please use 2 decimal places. (c) Who is relatively taller? The man is relatively taller. It is impossible to answer this question using the information given. They are the same relative height. The woman is relatively taller.

Answer 1

The Z-score for a women 6 feet tall is 3.2.

The Z-score for a man 6 feet tall is 1.07.

The correct option is D) The woman is relatively taller.

Explanation:

Consider the provided information.

Part(A)

The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.5 inches.

μ = 64 and σ = 2.5

We need to find the z-score for a woman who is 6 feet tall

1 feet = 12 inches

6 feet = 72 inches

`z=(\bar x -\mu)/(\sigma)`

Substitute the respective values.

`z=(72 -64)/(2.5)`

`z=3.2`

The Z-score for a women 6 feet tall is 3.2.

Part (B)

Men the same age have mean height 69 inches with standard deviation 2.8 inches.

μ = 69 and σ = 2.8

We need to find the z-score for a man who is 6 feet tall

6 feet = 72 inches

Thus,

`z=(72 -69)/(2.8)`

`z=1.07`

The Z-score for a man 6 feet tall is 1.07.

Part (C)

The z-score of women is greater thus the woman is relatively taller.

Hence, the correct option is D) The woman is relatively taller.