Question

In a certain​ city, the average​ 20- to​ 29-year old man is 69.8 inches​ tall, with a standard deviation of 3.1 ​inches, while the average​ 20- to​ 29-year old woman is 64.3 inches​ tall, with a standard deviation of 3.9 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 man ​, ___ ​, is smaller than the​ z-score for the woman ​, ___ ​, so he is relatively taller.

B. The​ z-score for the man ​,___ ​, is larger than the​ z-score for the woman ​, ___ ​, so he is relatively taller.

C. The​ z-score for the woman ​, ___ ​, is larger than the​ z-score for the man ​, ___ ​, so she is relatively taller.

D. The​ z-score for the woman ​, ___ ​, is smaller than the​ z-score for the man ​, ___ ​, so she is relatively taller.

Answer 1

Given In a certain​ city, the average​ 20- to​ 29-year old man is = 69.8 inches​ tall, with a standard deviation of = 3.1 ​inches, while the average​ 20- to​ 29-year old woman is =64.3 inches​ tall, with a standard deviation of = 3.9 inches.

Now to calculate Who is relatively​ taller we need to find Z score for both the scores as:

Z score for X = 75 inches man is calculated as:

for a X = 70-inch woman the Z score is calculated as:

B. The​ z-score for the man ​ 1.68  ​, is larger than the​ z-score for the woman ​, 1.46 ​, so he is relatively taller.