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Standard deviation for height means

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Men's height are normally distributed with mean 69.0 ins. and standard deviation 2.8 in

women 's heights are normally distributed with mean 63.6 ins and standard deviation 2.5 ins.

1. the standard doorway height is 80 in.
a. what percentage of men are too tall to fit through a doorway without bending , and what percentage of women are too tall to fit through a standard doorway without bending? Based on those results , does it appear that the current doorway design is adequate?

b. if a statistician designs a house so that all of the doorways have heights that are sufficient for all men except the tallest 5% , what doorway height would be used?

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The expert determines standard deviation for height means.

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Men's height are normally distributed with mean 69.0 ins. and standard deviation 2.8 in

Women 's heights are normally distributed with mean 63.6 ins and standard deviation 2.5 ins.

1. The standard doorway height ...

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