According to a study done by a university​ student, 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 12 randomly observed individuals exactly 6 do not cover their mouth when​ sneezing?

​(b) What is the probability that among 12 randomly observed individuals fewer than 4 do not cover their mouth when​ sneezing?

​(c) Would you be surprised​ if, after observing 12 ​individuals, fewer than half covered their mouth when​ sneezing? Why?

​(a) The probability that exactly 6 individuals do not cover their mouth is

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​(Round to four decimal places as​ needed.)

​(b) The probability that fewer than 4 individuals do not cover their mouth is

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​(Round to four decimal places as​ needed.)

​(​c) Fewer than half of 12 indiv