# Calculating mean and variance of probability

1. Feb 14, 2012

### bunnyrabid

1. The problem statement, all variables and given/known data

Given a 30% failure rate, what is the mean number of students who fail, and what is the variance? There are 8 students in the course.

2. Relevant equations

I think these are the correct equations:
Mean = Probability * Number of students
Variance = Sum from i=1 to 8 of pi(xi-Mean)^2

3. The attempt at a solution

So using the Mean formula I got 0.3*8=2.4
Using the variance formula I got
(0.3)(1-2.4)2+(0.3)(2-2.4)2+(0.3)(3-2.4)2+(0.3)(4-2.4)2+(0.3)(5-2.4)2+(0.3)(6-2.4)2+(0.3)(7-2.4)2+(0.3)(8-2.4)2
which is approximately equal to 23.184 (see variance formula here: wolfram alpha, then click approximate form )
Do I then square root to find the actual variance?

Thanks for any help!

2. Feb 14, 2012

### lanedance

the pi in your variance equation are not correct, you need to have a think about the probability distribution