Question

In a certain​ city, the average​ 20- to​ 29-year old man is 72.5 inches​ tall, with a standard deviation of 3.0 ​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 woman​, nothing​, is smaller than the​ z-score for the man​, nothing​, so she is relatively taller. B. The​ z-score for the woman​, nothing​, is larger than the​ z-score for the man​, nothing​, so she is relatively taller. C. The​ z-score for the man​, nothing​, is smaller than the​ z-score for the woman​, nothing​, so he is relatively taller. D. The​ z-score for the man​, nothing​, is larger than the​ z-score for the woman​, nothing​, so he is relatively taller

Answer 1

a).man:

H = 72.5, 0 = 3.0

the z score of a ​75-inch man is:-

$=\frac{X-\mu}{\sigma}=\frac{75-72.5}{3.0}\approx\mathbf{0.83}$

b).woman:

$\mu=64.3,\sigma=3.9$

the z score of a ​70-inch woman is:-

$=\frac{X-\mu}{\sigma}=\frac{70-64.3}{3.9}\approx\mathbf{1.46}$

c).The ​z-score for the woman​​ 1.46 is larger than the​ z-score for the man​ 0.83​, so she is relatively taller.

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