The average 20 - to 29-year old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20 - to 29-year old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75-inch man or a 70-inch woman?

a. The z-score for the woman is smaller, so she is relatively taller.

b. The z-score for the man is smaller, so he is relatively taller.

c. The z-score for the woman is larger, so she is relatively taller.

d. The z-score for the man is larger, so she is relatively taller.

Given Information:

The average 20-to-29 year old man = μ = 69.6 inches

standard deviation of 20-to-29 year old man = σ = 3.0 inches

20-to-29 year old man = x = 75 inches

The average 20-to-29 year old woman = μ = 64.1 inches

standard deviation of 20-to-29 year old woman = σ = 3.8 inches

20-to-29 year old woman = x = 70 inches

Required information:

Who is relatively taller, a 75 inch man or a 70 inch woman?

Step-by-step explanation:

First we have to find out the z-score of the 20-to-29 year old man and 20-to-29 year old woman.

For 20-to-29 year old man:

z = (x - μ) / σ

z = (75 - 69.6) / 3

z = 1.7

For 20-to-29 year old woman:

z = (x - μ) / σ

z = (70 - 64.1) / 3.8

z = 1.55

The z-score of the man is greater than the z-score of the woman. Therefore, man is relatively taller than woman.