According to a study done by a university student, the probability is a randomly selected individual will not cover his or her mouth while 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 12 randomly observed individuals exactly 4 do not cover their mouth when sneezing?
(b) What is the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing?
(c) Would you be surprised, after observing 12 individuals, fewer than half covered their mouth with sneezing? Why?