In a large corporation 65 of the employees are male A random

In a large corporation, 65% of the employees are male. A random sample of five
employees is selected. Use the Binomial probability tables to answer the following
questions. Show mathematical detail to receive full credit. You will receive a zero
just for providing the final answer.
a. What is the probability that the sample contains exactly three male employees?
b. What is the probability that the sample contains no male employees?
c. What is the probability that the sample contains more than three female employees?
d. What is the expected number of female employees in the sample?

Solution

n = 5

p = 0.65

q = 1-p

q = 0.35

a.

P(r=3) = nCr * p^r * q^(n-r)

P(r=3) = 5C3 * 0.65^3 * 0.35^2

P(r=3) = 0.3364

b.

P(r=0) = nCr * p^r * q^(n-r)

P(r=0) = 5C0 * 0.65^0 * 0.35^5

P(r=0) = 0.00525

c.

more than 3 female means 4 or 5 females that means 0 male or 1 male..

P(r=0 or r=1) = P(r=0) + P(r=1)

P(r=0) = nCr * p^r * q^(n-r)

P(r=0) = 5C0 * 0.65^0 * 0.35^5

P(r=0) = 0.0525

P(r=1) = nCr * p^r * q^(n-r)

P(r=1) = 5C1 * 0.65^1 * 0.35^4

P(r=1) = 0.0487

P(r=0 or r=1) = P(r=0) + P(r=1)

P(r=0 or r=1) = 0.00525 + 0.0487

P(r=0 or r=1) = 0.054

d.

expected number of male = n * p = 5 * 0.65 = 3.25

So,

expected number of women = 5 - 3.25 = 1.75