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 5 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?

Explanation / Answer

p = 0.267

n = 16

P(X = x) = 16Cx * 0.267x * (1 - 0.267)16-x

a) P(X = 4) = 16C4 * 0.2674 * 0.73312 = 0.2225

b) P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= 16C0 * 0.2670 * 0.73316 + 16C1 * 0.2671 * 0.73315 + 16C2 * 0.2672 * 0.73314 + 16C3 * 0.2673 * 0.73313 + 16C4 * 0.2674 * 0.73312

= 0.5685

c) P(X < 8) = 0.9605

Since the probability is greater than 0.95, this is unusual. So yes i would be surprised

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