Men\'s heights are normally distributed with mean 70.1 in and standard deviation
ID: 3222976 • Letter: M
Question
Men's heights are normally distributed with mean 70.1 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 s that all of the doorways have heights that are sufficient for all men except the tallest 5%, what doorway height would be used? 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.) The statistician would design a house with doorway height __________ in.Explanation / Answer
a) P(X>80)=1-P(Z<(80-70.1)/2.8)=1-P(Z<3.5357)=1-0.9998 =0.0002 =~0.02%
b)P(X>80)=1-P(Z<(80-63.5)/2.5)=1-1 =0.00%
c)for tallest 5% , z=1.6449
hence corresponding height=70.1+1.6449*2.8 =74.71 In