According to a study done by Nick Wilson of Otago University​ Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.

​(​a) Using the binomial​ distribution, what is the probability that among 10 randomly observed​ individuals, exactly 8 do not cover their mouth when​ sneezing?

Answer:

Given:

The probability of success, $p=0.267$

The sample size, $n=10$

Solution:

→ The probability that among 10 randomly observed​ individuals, exactly 8 do not cover their mouth when​ sneezing :

$$P(x=8)=(\genfrac{}{}{0ex}{}{n}{x})p^x(1–p{)}^{n–x}{|}_{x=8}$$ $$=(\genfrac{}{}{0ex}{}{10}{8}){0.267}^8(1–0.267{)}^{10–8}$$ $$=0.0006$$