According to a study done by a university student, the probability a randomly se

Question

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 16 randomly observed individuals exactly 4 do not cover their mouth when sneezing? (b) What is the probability that among 16 randomly observed individuals fewer than 3 do not cover their mouth when sneezing? (c) Would you be surprised if, after observing 16 individuals, fewer than half covered their mouth when sneezing? Why? (a) The probability that exactly 4 individuals do not cover their mouth is 0.2225 Round to four decimal places as needed.) (b) The probability that fewer than 3 individuals do not cover their mouth is Round to four decimal places as needed.)

Explanation / Answer

b) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 16c0 * 0.2670 * 0.73316 + 16c1 * 0.2671 * 0.73315 + 16c2 * 0.2672 * 0.73314 = 0.1580

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