Men\'s heights are normally distributed with mean 68.7 in and standard deviation
ID: 3290072 • Letter: M
Question
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. a. 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? 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? a. The percentage of men who are too tall to fit through a standard door without bending is % (Round to two decimal places as needed.) The percentage of women who are too tall to fit through a standard door without bending is % (Round to two decimal places as needed.) b. The statistician would design a house with doorway height in. (Round to the nearest tenth as needed.)Explanation / Answer
a) Percentage of men too tall to fit
= P(X > 80)
= P(z > (80 - 68.7)/2.8)
= P(z > 4.04)
= 0.00%
Similarly,
Percentage of women too tall to fit = 0.00%
b) z cutoff for tallest %, z = 1.645
Hence,
Required doorway height
= 68.7 + 1.645*2.8
= 73.3 inches