Question

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that less than three take the discount (round answers to three decimal places, for example, 0.xxx)

Answer 1

0.551

Explanation:

Let no. of people who take discount = x

Using binomial distribution, N c X. p^x. q^(n-x)

p : customer getting discount = 0.3, q : customer not getting discount = 0.7 n : no. of customers = 8

Probability that x < 3 : Prob (x=0) + Prob (x=1) + Prob (x=2)

= 8 c 0. (0.3)^0 . (0.7)^8 + 8 c 1. (0.3)^1 . (0.7)^7 + 8 c 2. (0.3)^2 . (0.7)^6

0.05764801 + 0.19765032 + 0.29647548

0.551