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 10 randomly observed individuals exactly 7 do not cover their mouth when​ sneezing? ​(​b) What is the probability that among 10 randomly observed individuals fewer than 4 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

Solution:

Given:

p = probability of individual will not cover his or her mouth when sneezing = 0.267

We can find all probabilities using Binomial distribution.

a) We have to find P(X= 7) when n = 10

Using Binomial formula,

Therefore,

b) We have to find P(X<4) when n = 10

P(X<4) = P(X3)

Therefore,

P(X≤3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

=0.0448+0.1631+0.2673+0.2597

=0.7349

Hence, P(X<4) = 0.7349

c) We have to find P(X<5) when n=10

P(X<5) = P(X4)

Therefore,

P(X≤4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

=0.0448+0.1631+0.2673+0.2597+0.1655

=0.9004

I would not surprised if after observing 10 ​individuals, fewer than half covered their mouth when​ sneezing as probability is high.

Done