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?

Question

Raphael Stevenson

Mathematics

5 February, 10:13

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?

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Answers (1)

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Kyler Jensen · Answer 1

the man

Step-by-step 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.