Question

Telesales representatives make a sale 5% of the time. Find the probability of making a sale in: a.) 10 calls. b.) More than 3 or less than 9. c.) Greater than 1.

Answer 1

Here

Pr(Telesales representatives make a sale) = 0.05

Pr(Not making a sale in a call) = 0.95

Here if x is the number of calls required to make first sale. so x will follow geometric distribution with probability of success is 0.05.

(a) Pr(Making a sale in 10 calls) = 1 - Pr(Not making a sale in 10 calls)

= 1 - (1 - 0.05)¹⁰

= 1 - 0.95¹⁰ = 0.4013

(b) Probability of making a sale in more than 3 or less than 9 calls that means making a sale in 4th, 5th, 6th, 7th or in 8th call.

Pr(Making a sale in 4th,5th,6th,7th or in 8th call) = 1 - Pr(no sale in these 6 times )

= 1 - 0.95⁶ = 0.2649

(c) Pr(Making a sale in greater than 1 call) = 1 - Pr(Making a sale in first call)

= 1 - 0.05 = 0.95