Answer :

Final answer:

The probability that a husband is taller than 72 inches when the wife's height is 68 inches cannot be calculated without additional information about the distribution of the husband's height, specifically the mean and standard deviation of the male height distribution.

Explanation:

To calculate the probability that a husband is taller than 72 inches given that the wife's height is 68 inches, we need to refer to a normal distribution, since human heights are usually modeled using this distribution. However, the information given about the wife's height being 68 inches does not directly relate to the probability of the husband's height. The husband's height would typically be influenced by the population's mean height for males and the standard deviation.

If we assume that the husband's height follows X~ N(66, 2.5), which is a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches, we can calculate this probability using z-scores or a standard normal distribution table. By converting 72 inches to a z-score, we can find the probability that the husband's height exceeds this value. This would be calculated as P(X > 72) where X is the husband's height.

Without the necessary information about the distribution of the husband's heights, we cannot provide a numerical answer to the probability in question. The question requires data on the population mean and standard deviation for the husband's height, not the height of the wife.

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Rewritten by : Barada