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 people’s habits as they sneeze.
(a) What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?
(b) What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth?
(c) Would you be surprised if, after observing 10 individuals, fewer than half covered their mouth when sneezing? Why?