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 12 randomly observed individuals exactly 5 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?

Round answers to 4 decimal points, on question C provide if it would/would not be surprising and is/is not surprising and percentage.

Explanation / Answer

a)

P(not covering mouth) = 0.267

P(covering mouth) = 1-0.267 = 0.733

P(exactly 5 do not cover out of 12) = C(12,5)*(0.267^5)*(0.733^7) = 0.1222

b)

P(fewer than 4 do not cover mouth) = C(12,0)*(0.267^0)*(0.733^12) +C(12,1)*(0.267^1)*(0.733^11)+C(12,2)*(0.267^2)*(0.733^10)+C(12,3)*(0.267^3)*(0.733^9)

=1*(0.267^0)*(0.733^12)+12*(0.267^1)*(0.733^11) + 66*(0.267^2)*(0.733^10)+220*(0.267^3)*(0.733^9)

=0.5957

c)

P(fewer than half covering their mouth) = 0.0206 = 2.06%

It would be surprising as the % is less than 5%

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