Problem 2RE

In Exercises, assume that 40% of the population has brown eyes (based on data from Dr. P. Sorita at Indiana University).

Brown Eyes Find the probability that among six randomly selected people, exactly four of them have brown eyes.

Problem 2RE

Answer:

Step1 of 1:

We have In Exercises, assume that 40% of the population has brown eyes (based on data from Dr. P. Sorita at Indiana University) that is p = 40% = 0.40.we need to find the probability that among six randomly selected people, exactly four of them have brown eyes.

Here,

P = 0.40 n = 6

Consider a random variable “x” follows binomial distribution with sample size “n” and proportion “p”.

i,e.X B(n, p)

Where,

n = 6 and p = 0.40.

q = 1 - p

= 1 - 0.40

= 0.6.

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

Now,

The probability that among six randomly selected people, exactly four of them have brown eyes is given by

P(x) =

P(x = 4) =

= 150.02560.36

= 0.1382.