A survey found that women\'s heights are normally distributed with mean 62.1 in.

Question

A survey found that women's heights are normally distributed with mean 62.1 in. and standard deviation 2.2 in. The survey also found that men's heights are normally distributed with a mean 67.3 in. and standard deviation 2.9.

The percentage of women who meet the height requirement is 99.72%. The percentage of men who meet the height requirement is 99.86%.

If the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women, what are the new height requirements?

The new height requirements are at least _____ in. and at most _____ in.

Explanation / Answer

Solution:- Given that

women : mean = 62.1 in, standard deviation = 2.2 in

men : mean = 67.3 in, standard deviation = 2.9 in

These turn out to be: +1.645 and -1.645

Men : tallest 5% = 1.645

men -- 67.3 + (1.645*2.9) = 72.0705

Women : shortest 5% = -1.645

Women --- 62.1 - (1.645*2.2) = 58.481

the new height requirements are at least 58.481 in. and at most 72.0705 in.

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