Question

The probability of a getting a new sales contract with any given client is 0.29. A sales representative works with 18 clients this week. What is the expected number of contracts the sales representative will get this week?

Answer 1

The expected number of contracts the sales representative will get this week is 5.22

Explanation:

For each client, there are only two possible outcomes. Either there is a sales contract, or there is not. The probability of having a sale contract with each client is independent of other clients. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

`E(X) = np`

In this problem, we have that:

`n = 18, p = 0.29`

What is the expected number of contracts the sales representative will get this week?

`E(X) = np = 18*0.29 = 5.22`

The expected number of contracts the sales representative will get this week is 5.22