Question

1. It is estimated that 40% of MBA graduates are women. A company advertises a position for an MBA graduate, and draws up a list of five candidates for a final interview. Assume that those 5 individuals can be regarded as a random sample of all MBA graduates.
   1. What is the probability that there is no woman on the list?

2. What is the probability that the majority of those on the list are women?

3. What is the probability that the number of women on the list is between one and four (excluding one and four)?

4. How many women would you expect to be on the list?

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

Here, sample size, n = 5

P(woman), p = 0.4

q = 1 - p = 0.6

a) P(no woman on list), P(0) = 0.6⁵

= 0.07776

b) P(majority are women) = P(3 or more women)

= P(3) + P(4) + P(5)

= 5C3x0.4³x0.6² + 5x0.4⁴x0.6 + 0.4⁵

= 0.2304 + 0.0768 + 0.01024

= 0.31744

c) P(between one and four, excluding one and four) = P(2) + P(3)

= 5C2x0.4²x0.6³ + 0.2304

= 0.3456 + 0.2304

= 0.5760

d) Expected number of women to be on list = np

= 5x0.4

= 2