According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe 300 randomly selected individuals’ habits as they sneeze.

(a) Use the normal approximation to the binomial to approximate the probability that of the 300 randomly observed individuals exactly 100 do not cover the mouth when sneezing.

(b) Use the normal approximation to the binomial to approximate the probability that of the 300 randomly observed individuals fewer than 75 do not cover the mouth.

(c) Would you be surprised if, after observing 300 individuals, more than 100 did not cover the mouth when sneezing? Why?