This is a central limit theorem question, so let if the -th samped voter

votes A, and otherwise. then the mean for is

and the variance is

So the number of votes for A in the sample is:

which approximatly has a normal distribution with mean , and variance .

So now we want the probability that or more will vote A. As we have

a continuous distribution modelling a discrete we ask what is the probability

of a value greater than occuring from a normal distribution with mean and variance .

The z-score for this problem is:

which we look up in a standard normal table to get a probability of .

Note if we had been asked for the probability of more than 50 voted for A this would drop to

(If this were not a CLT question I would have used a binomial distribution to

model the distribution of the number of votes for A in the sample, but when the

normal approximation is used for the binomial the answer is exactly the same

as we get with the above argument)

RonL