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 3.9 inches. who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman?

Answer 1

the man

Explanation:

The wording "relatively taller" in this context is presumed to be a reference to the corresponding percentile or z-score. By hand, the z-score is easier to calculate.

z = (x - μ)/σ

For the man,

... z = (75 -69.8)/3.2 = 1.625

For the woman,

... z = (70 -64.3)/3.9 ≈ 1.462

The man's z-score is higher, so he is taller than a larger percentage of the male population than the woman is of the female population.

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If you're doing this by calculator, you can let it show you the percentile rank of each height. The man is in the 95th percentile; the woman the 93rd percentile. So, the man is relatively taller.