Question

In a certain​ city, the average​ 20- to​ 29-year old man is 69.8 inches​ tall, with a standard deviation of 3.2 ​inches, while the average​ 20- to​ 29-year old woman is 64.3 inches​ tall, with a standard deviation of 3.8 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.)

1. The​ z-score for the woman​___is larger than the​ z-score for the man​​___so she is relatively taller.
2. The​ z-score for the man​___ is smaller than the​ z-score for the woman​__ so he is relatively taller.
3. The​ z-score for the woman​___nothing​, is smaller than the​ z-score for the man​___ so she is relatively taller.
4. The​ z-score for the man​___ is larger than the​ z-score for the woman​___nothing​, so he is relatively taller.

Answer 1

For man

Here, μ = 69.8, σ = 3.2 and x = 75. We need to compute P(X <= 75). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (75 - 69.8)/3.2 = 1.63

For woman

Here, μ = 64.3, σ = 3.8 and x = 70. We need to compute P(X <= 70). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (70 - 64.3)/3.8 = 1.5

The​ z-score for the man​ 1.63 is larger than the​ z-score for the woman 1.5​, so he is relatively taller.