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 . Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze. ​(​a) What is the probability that among randomly observed individuals exactly do not cover their mouth when​ sneezing

Answer 1

Complete 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 18 randomly observed individuals exactly 6 do not cover their mouth when sneezing?

Answer:

`P(X=6)=(0.162)`

Explanation:

From the question we are told that:

Sample size
`n=18`

Probability
`P=0.267`

No. that do not cover their mouth when sneezing
`x=6`

Generally the equation for The Binomial distribution is mathematically given by

Parameters

B(18,0.267)

Therefore

`P(X=x)=(18..x)(0.267)^x(1-0.267)^(18-x)`

Where

`x=6`

Therefore

`P(X=6)=(18..6)(0.267)^6(1-0.267)^(18-6)`

`P(X=6)=(0.162)`