Questions: In a certain city, the average 20- to 29-year old man is 69.4 inches tall, with a standard deviation of 3.2 inches, while the average 20 - to 29 -year old woman is 64.5 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 man, , is larger than the z -score for the woman, so he is relatively taller. B. The z-score for the man, , is smaller than the z-score for the woman, so he is relatively taller. C. The z-score for the woman, , is smaller than the z-score for the man so she is relatively taller. D. The z-score for the woman, , is larger than the z-score for the man, so she is relatively taller.

In a certain city, the average 20- to 29-year old man is 69.4 inches tall, with a standard deviation of 3.2 inches, while the average 20 - to 29 -year old woman is 64.5 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 man, , is larger than the z -score for the woman, so he is relatively taller. B. The z-score for the man, , is smaller than the z-score for the woman, so he is relatively taller. C. The z-score for the woman, , is smaller than the z-score for the man so she is relatively taller. D. The z-score for the woman, , is larger than the z-score for the man, so she is relatively taller.
Transcript text: In a certain city, the average 20- to 29-year old man is 69.4 inches tall, with a standard deviation of 3.2 inches, while the average 20 - to 29 -year old woman is 64.5 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 man, $\square$ , is larger than the z -score for the woman, $\square$ so heis relatively taller. B. The z-score for the man, $\square$ , is smaller than the $z$-score for the wontin, $\square$ so heis relatively taller. C. The $z$-score for the woman, $\square$ , is smaller than the $z$-score for the man $\square$ so sheis relatively taller. D. The $z$-score for the woman, $\square$ , is larger than the $z$-score for the man, $\square$ so sheis relatively taller.
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Solution

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Solution Steps

Step 1: Calculate the Z-score for the man

Using the formula $Z_m = \frac{H_m - M_{avg}}{M_{sd}}$, where $H_m$ is the man's height, $M_{avg}$ is the average height of men, and $M_{sd}$ is the standard deviation of men's heights, we find that $Z_m = \frac{75 - 69.4}{3.2} = 1.75$.

Step 2: Calculate the Z-score for the woman

Using the formula $Z_w = \frac{H_w - W_{avg}}{W_{sd}}$, where $H_w$ is the woman's height, $W_{avg}$ is the average height of women, and $W_{sd}$ is the standard deviation of women's heights, we find that $Z_w = \frac{70 - 64.5}{3.9} = 1.41$.

Final Answer:

The man is relatively taller than the woman in terms of their respective gender and age group distributions.

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