Question

A company begins a direct mailing program. The marketing manager estimates that about 10% of the people receiving the package will place an order. The package is sent to 200 people.

What is the expected value and standard deviation of the distribution?

What is the probability that more than 30 people will place an order?

What is the probability that the number of orders will be between 20 and 30 inclusive?

Answer 1

The exact distribution given here is:

a) The mean and standard deviation are computed as:

Therefore 20 is the mean and 4.24 is the standard deviation.

b) Therefore the above distribution could be approximated to a normal distribution as:

The probability here is computed as:

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get the above probability as:

Therefore 0.0091 is the required probability here.

c) The required probability here is:

Applying the continuity correction, we get here:

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.4465 is the required probability here.