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)