A) Use the inverse normal idea to get the value of a such that Pr(X > a) = 0.25. This will give the minimum height of the door.

B) Find p = Pr(X > 76). Multiply this number by 5000.

The reason for this is that if Y is the random variablenumber of people who bump their head, then Y ~ Binomial(n = 5000, p). And you know E(Y) = np ......