Question

Suppose that of all voters in Florida, 40% (p=.4) are in favorite of candidate Brown for Governor. Pollsters take a sample of 2400 voters. What proportion of the sample would be expected to favor candidate Brown? (show your work)

Answer 1

Let X be the random variable that a person is in favor of candidate Brown .

Then X~ Ber ( p = 0.4 )

Now , if n  samples are drawn from the population of X , the number of people in favor of candidate Brown ,

follows Binomial distribution .

Y~ Bin( n, p)

and we know E(Y) = np

So, expected proportion of the sample in favor of candidate Brown , E( Y/n) = p = 0.4 , same as the population proportion .

[Although it is very trivial , calculations are not needed at all ]