Question

Researchers claim that 8% of people have blue eyes. Suppose the researchers' claim is true. Mrs. Greene has a Geometry class with 40 students. What is the probability that exactly 5 of them have blue eyes? 0 0.0573 0.1023 0.1165 0.9020

Answer 1

Probability that exactly 5 of them have blue eyes is 0.1165.

Explanation:

We are given that Researchers claim that 8% of people have blue eyes. Suppose the researchers' claim is true. Mrs. Greene has a Geometry class with 40 students.

The above situation can be represented through Binomial distribution;

`P(X=r) = \binom{n}{r}p^(r) (1-p)^(n-r) ; x = 0,1,2,3,.....`

where, n = number of trials (samples) taken = 40 students

r = number of success = exactly 5

p = probability of success which in our question is % of people

having blue eyes, i.e; 8%

LET X = Number of students having blue eyes

So, it means X ~
`Binom(n= 40,p=0.08)`

Now, Probability that exactly 5 of them have blue eyes is given by = P(X = 5)

P(X = 5) =
`\binom{40}{5}* 0.08^(5) * (1-0.08)^(40-5)`

=
`658008 * 0.08^(5) * 0.92^(35)`

= 0.1165

Therefore, Probability that exactly 5 of them have blue eyes is 0.1165.