Respuesta :
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;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
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 ~ [tex]Binom(n= 40,p=0.08)[/tex]
Now, Probability that exactly 5 of them have blue eyes is given by = P(X = 5)
P(X = 5) = [tex]\binom{40}{5}\times 0.08^{5} \times (1-0.08)^{40-5}[/tex]
= [tex]658008 \times 0.08^{5} \times 0.92^{35}[/tex]
= 0.1165
Therefore, Probability that exactly 5 of them have blue eyes is 0.1165.
