Question

It is known that 40 percent of the customers of a mortgage company default on their payments. A sample of 15 customers is selected. What is the probability that 6 or more customers in the sample will default on their payments

Answer 1

p = 0.4

n = 15

P(X = x) = nCx * p^x * (1 - p)^{n - x}

P(X > 6) = 1 - P(X < 6)

              = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5))

              = 1 - (15C0 * (0.4)^0 * (0.6)^15 + 15C1 * (0.4)^1 * (0.6)^14 + 15C2 * (0.4)^2 * (0.6)^13 + 15C3 * (0.4)^3 * (0.6)^12 + 15C4 * (0.4)^4 * (0.6)^11 + 15C5 * (0.4)^5 * (0.6)^10)

             = 1 - 0.4032

             = 0.5968