Question

In a certain​ city, the average​ 20- to​ 29-year old man is 69.669.6 inches​ tall, with a standard deviation of 3.23.2 ​inches, while the average​ 20- to​ 29-year old woman is 64.564.5 inches​ tall, with a standard deviation of 3.83.8 inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman? Find the corresponding​ z-scores. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman? Select the correct choice below and fill in the answer boxes to complete your choice. ​(Round to two decimal places as​ needed.)

a. The​ z-score for the manman​, nothing​, is larger than the​ z-score for the womanwoman​, nothing​, so hehe is relatively taller.
b. The​ z-score for the womanwoman​, nothing​, is larger than the​ z-score for the manman​, nothing​, so sheshe is relatively taller.
c. The​ z-score for the manman​, nothing​, is smaller than the​ z-score for the womanwoman​, nothing​, so hehe is relatively taller.
d. The​ z-score for the womanwoman​, nothing​, is smaller than the​ z-score for the manman​, nothing​, so sheshe is relatively taller.

Answer 1

The 75-inch man is relatively taller than the 70-inch woman (a).

Step-by-step explanation:

To determine who is relatively taller, we need to compare the z-scores of a 75-inch man and a 70-inch woman.

• The z-score formula is (X - μ) / σ, where X is the given height, μ is the average height, and σ is the standard deviation.
• For the 75-inch man, the z-score is (75 - 69.6) / 3.2 = 1.75.
• For the 70-inch woman, the z-score is (70 - 64.5) / 3.8 = 1.45.
• Since the z-score for the man is larger than the z-score for the woman, the man is relatively taller.

Answer 2

The z-score is given by:
Z-score=(x-μ)/σ
where:
μ=mean
σ=std deviation
From the information:
mean for 20-29 year old man is μ=69.669 and std deviation is σ=3.23
mean for 20-29 year old woman is μ=64.564 and the std deviation is σ=3.83

the z-score for 75 inch men is:
z-man=(75-69.669)/3.23=1.651

the z-core for 70 inch woman:
z-woman=(70-64.564)/3.83
=1.42
From the above we conclude that the z-score for the man is relatively larger than that of the women, this means that the man is taller.
The answer is A.