Question

When an opinion poll calls landline telephone numbers at random, approximately 30% of the numbers are working residential phone numbers. The remainder are either non-residential, non-working, or computer/fax numbers. You watch the random dialing machine make 20 calls. What is the mean number of calls that reach a person? Standard deviation?

Answer 1

Mean = 6

Standard Deviation = 4.2

Explanation:

This is a binomial probability distribution problem.

The mean has formula:

`\mu = np`

The standard deviation has formula:

`\sigma=np(1-p)`

Where n is the number of calls [20]

p is the probability of success [30=0.3]

Let's put these into the formula:

`\mu=np\\\mu=(20)(0.3)\\\mu=6`

and

`\sigma=np(1-p)\\\sigma=(20)(0.3)(1-0.3)\\\sigma=(20)(0.3)(0.7)\\\sigma=4.2`