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Answer :
Final answer:
To determine the correct option, we need to calculate the z-scores for the given heights and compare them to the cumulative probability to find the proportion of men shorter than that height. The correct answer is (a), 65.5 inches.
Explanation:
To determine which option is correct, we need to calculate the z-scores for the given heights and compare them to the cumulative probability to find the proportion of men shorter than that height.
(a) The z-score for 65.5 inches is (65.5 - 68) / 2.5 = -1.1. The proportion of men shorter than this height is approximately 0.1359.
(b) The z-score for 68 inches is (68 - 68) / 2.5 = 0. The proportion of men shorter than this height is 0.5.
(c) The z-score for 70.5 inches is (70.5 - 68) / 2.5 = 0.9. The proportion of men shorter than this height is approximately 0.8159.
Comparing the proportions, we can see that half of all young men are shorter than 65.5 inches, so the correct answer is (a).
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