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 expected number of customers that will take the discount (round answers to three decimal places, for example, 0.xxx)?

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 at least three take the discount (round answers to three decimal places, for example, 0.xxx)?

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 exactly three take the discount (round answers to three decimal places, for example, 0.xxx)?

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

Let , X be the number of customer use the discount.

Here , the X has a binomial distribution with parameter n=8 and p=030

Now ,q=1-p=0.70

The probability mass function of X is ,

= 0 ; otherwise

a) E(X)=np=8*0.30=2.400

Therefore , the expected number of customers that will take the discount is 2.400

b)

; From binomial distribution probability table

Therefore , the probability that at least three take the discount is 0.448

c)

  ; From binomial distribution probability table

Therefore , the probability that exactly three take the discount is 0.254

d)

; From binomial distribution probability table

Therefore , the probability that less than  three take the discount is 0.552