(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 :
$$P(x = 8) = \binom{n}{x} p^x (1 – p)^{n – x} \bigg|_{x = 8}$$ $$= \binom{10}{8} 0.267^8 (1 – 0.267)^{10 – 8}$$ $$= 0.0006$$
