Question

In a large corporation, 65% of the employees are male. A random sample of 5 employees is selected. We wish to determine the probability of selecting exactly 3 males. Use an appropriate probability distribution to answer the following:

(a) Define the variable of interest for this scenario.

(b) What is the probability that the sample contains exactly three male employees?

(c) Justify the suitability of the probability distribution that you used to solve part (a).

(d) What is the expected number of male employees in the sample?

Answer 1

p = probability that the employees are male = 0.65

n = number of employees selected randomly = 5

a) Define random variable X: number of male employees.

X follows Binomial distribution with n = 5 and p = 0.65

If X follows Binomial distribution with n and p

                  x = 0,1,2,............n

Where

                              n! = 1*2*3*........*n

Here

                x = 0,1,2,3,4,5

b)

Here we have to find P(X = 3)

                      

                      

                     

                      = 10 * 0.274625 * 0.1225

                      = 0.3364                  (Round to 4 decimal)

The probability that the sample contains exactly three male employees is 0.3364

c)

If X follows Binomial distribution with n and p

                  x = 0,1,2,............n

Where

                              n! = 1*2*3*........*n

Here

                x = 0,1,2,3,4,5

d) Expected number of male employees:

E(X) = n * p

        = 5 * 0.65

        = 3.25

Expected number of male employees = 3.25