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 8 do not cover their mouth when​ sneezing?

Answer 1

The probability of exactly 8 out of 12 individuals not covering their mouth when sneezing is determined using the binomial probability formula with a given success probability of 0.267.

Step-by-step explanation:

The probability that among 12 randomly observed individuals exactly 8 do not cover their mouths when sneezing is calculated using the binomial probability formula, which for this question is represented as: P(X = n) = (C(n, k)) * (p^k) * ((1-p)^(n-k)), where 'C(n, k)' represents the combination of 'n' items taken 'k' at a time, 'p' is the probability of an individual event, 'k' is the number of successes, and 'n' is the total number of events.

Given the probability 'p' that an individual does not cover their mouth is 0.267, the probability of exactly 8 out of 12 individuals not covering their mouth can be calculated as P(X = 8) = (C(12, 8)) * (0.267^8) * ((1-0.267)^(12-8)).