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1. Men's heights are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches, while women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches.
(a) What percentage of men must duck when walking through a door that is 72 inches high?
(b) What percentage of women must duck when walking through a door that is 70 inches high?
(c) What door height would allow at least 95% of men to walk through the door that is 72 inches high without ducking?

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