Statistics: Mean and Standard Deviation

[nessa]

Homework Statement

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizen are chosen, what is the standard deviation of the number favoring the substation?

Homework Equations

I know that my mean is 15 and the probiblilty is 80 but how do I get the standard deviation.

The Attempt at a Solution

 

[nessa]

The answer is 12.

Do NOT simply give out the answer. In fact, don't give the answer at all in the homework section! (Not even a wrong answer! The question was about the standard deviation, not the mean.)
(Editted by HallsofIvy)

 

[HallsofIvy]

Homework Statement

In a recent survey, 80% of the community favored building a police substation in their neighborhood. If 15 citizen are chosen, what is the standard deviation of the number favoring the substation?

Homework Equations

I know that my mean is 15 and the probiblilty is 80 but how do I get the standard deviation.

The Attempt at a Solution

You need to go back and read the basic definitions! The number of people surveyed is 15. That surely does not mean that they will expect all 15 to favor the substation! The expected value (mean) is not 15.

This is a binomial distribution with p= .8, q= 1- .8= .2, and n= 15. I'm sure you textbook tells you that the mean of a binomial distribution is np and the standard deviation is $\sqrt{npq}$.