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 t
he 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?
1 answer:
Answer:
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.
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