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 .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 3 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?

Answer 1

The probability that a randomly selected individual will not cover his or her mouth when sneezing is p = 0.267

Let X denotes the number of observed individuals who do not cover their mouth when​ sneezing out of 12 randomly observed individuals.

X ~ Binomial(n = 12, p = 0.267)

The probability mass function of X is

Now,

a) The probability that among 12 randomly observed individuals exactly 6 do not cover their mouth when​ sneezing

b) The probability that among 12 randomly observed individuals fewer than 3 do not cover their mouth when​sneezing

c) The probability that among 12 randomly observed individuals fewer than half covered their mouth when​ sneezing