Question

ccording 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 10 randomly observed individuals exactly 8 do not cover their mouth when​ sneezing? ​(b) What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing? ​(c) Would you be surprised​ if, after observing 10 ​individuals, fewer than half covered their mouth when​ sneezing? Why?

Answer 1

a) What is the probability that among 10 randomly observed individuals exactly 8 do not cover their mouth when​ sneezing?

This is a binomial probability.

b) What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when​ sneezing?

Here we need to find

P(X<3) = 1 - P(X=0) + P(X=1) +P(X=2)

P(X<3) = 1 - (P(X=0) + P(X=1) +P(X=2)) = 1 - (0.448 + 0.1631+0.2673) = 0,1216

​(c) Would you be surprised​ if, after observing 10 ​individuals, fewer than half covered their mouth when​ sneezing? Why?

Out of 10 individuals, the expected number of individuals who do not cover their face= (10 * 0.267) = 2.67

Hence about 3 individuals are expected not to cover their face. Hence it would be surprizing if, after observing 10 ​individuals, fewer than half covered their mouth when​ sneezing