Question

Four percent of the customers of a mortgage company default on their payments. a sample of five customers is selected. what is the probability that exactly two customers in the sample will default on their payments?

Answer 1

We can use the formula for binomial distribution in calculating for the probability that exactly two customers out five will default on their payments.

The formula is: P(r) = nCr*q^(n-r)*p^r
Where:
n = sample size, 5
r = successes, 2
q = failure rate, 96% = 0.96
r = success rate, 4% = 0.04

Substituting on the formula:
P = 5C2*0.96^3*0.04^2
P = 0.0142 or 1.42%