Question

A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing. What is the expected number (mean) of sales of this store from this sample of 30?

Answer 1

Answer:

The expected number of sales of this store from this sample of 30 is 6.

Step-by-step explanation:

For each prospect, there are only two possible outcomes. Either there is a trade, or there is not. Prospects are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

The expected value of the binomial distribution is:

$E(X) = np$

A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability.

This means that $p = 0.2$

Suppose 30 prospects are randomly selected from a city-wide mailing.

This means that $n = 30$

What is the expected number (mean) of sales of this store from this sample of 30?

$E(X) = np = 30*0.2 = 6$

The expected number of sales of this store from this sample of 30 is 6.