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Men’s heights are normally distributed with mean 68.7 in and standard deviation of 2.8 in.

    Men’s heights are normally distributed with mean 68.7 in and standard deviation of 2.8 in. ​Women’s heights are normally distributed with mean 63.5 in and standard deviation of 2.5 in. The standard doorway height is 80 in.

    1. What percentage of men are too tall to fit through a standard doorway without​ bending, and what percentage of women are too tall to fit through a standard doorway without​ bending?
    2. 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?