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

Answer:

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

Step-by-step 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) =  $\binom{40}{5}\times 0.08^{5} \times (1-0.08)^{40-5}$

                      =  $658008 \times 0.08^{5} \times 0.92^{35}$

                      = 0.1165

                

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