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

4

do not cover their mouth when​ sneezing?

​(​b)

What is the probability that among

10

randomly observed individuals fewer than

6

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 = the probability a randomly selected individual will not cover his or her mouth when sneezing = 0.267

n = 10

a) We have to find P(X=4) = ...?

Binomial probability fomula,

Therefore, P(X= 4 )

= 0.1655

Hence, the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when​ sneezing = 0.1655

b)

We have to find P(X<6) = ...?

Here, P(X<6) =P(X5)

So, P(X5) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

=0.0448+0.1631+0.2673+0.2597+0.1655+0.0724

=0.9728

Hence, the probability that among 10 randomly observed individuals fewer than 6 do not cover their mouth when​ sneezing = 0.9728

c)

We have to find P(X<5) = ...?

Here, P(X<5) =P(X4)

So, P(X4) = 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

Hence, Probability that after observing 10 ​individuals, fewer than half covered their mouth when​ sneezing = 0.9004

I would be not surprising as probability is high.

Done