Suppose that a doorway being constructed is to be used by a class of people whose heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches.

A) How high should the doorway be, without causing more than 25% of the people to bump their heads?

B) If the height of the door is fixed at 76 inches, how many persons out of 5000 are expected to bump their heads?