55% support, 40 voters at random, X = voters that support find the mean and variance of X.

Question

In a survey, 55% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the mean and variance of X.

Answer 1

mean=(number in the sample)*(probability) for a binomial distribution=40*0.55=22. This is an application of the binomial distribution µ=np where µ is the mean, n the sample size and p the probability. The variance is given by np(1-p)=40*0.55*0.45=9.9.