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. Complete parts (a) through (c). (a) What is the probability that among 12 randomly observed individuals, exactly 8 do not cover their mouth when sneezing? Using the binomial distribution, the probability is (Round to four decimal places as needed.) (b) What is the probability that among 12 randomly observed individuals, fewer than 4 do not cover their mouth when sneezing? Using the binomial distribution, the probability is (Round to four decimal places as needed.) (c) Would you be surprised if, after observing 12 individuals, fewer than half covered their mouth when sneezing? Why? be surprising, because using the binomial distribution, the probability is , which is 0.05 (Round to four decimal places as needed.)