Question 1091258
z=(x-mean)/sd
want z for a mean of 69.4
percent of men over 72 inches
z=(72-69.4)/2.2=1.182
z <+1.182 is the probability desired,of 0.8814 or 88.1%
for 99%, need the value of z (0.99), which is +2.328
multiply that by the sd and get 5.1216. That is the difference between the mean and the height of the door.
The door height needs to be 69.4+5.1 or 74.5 inches.