Reference no: EM132377623

In political polling, randomly selected voters are asked whether they would vote for a particular candidate. A random variable X

X is defined that takes a value of 1 if the answer is 'yes', and a value of 0 if the answer is 'no'. Note that X

X has a Bernoulli distribution. The variance of the Bernoulli distribution is known to be p(1-p)

p(1-p) where p=E(X)

p=E(X) is the probability that a randomly selected voter would vote for the candidate. Since the variance must be finite, if a large number of voters are surveyed independently, a central limit theorem dictates that the mean value of the random variables generated will be approximately normally distributed.

1. Suppose you have been commissioned to conduct a poll to determine the popularity of a candidate who is expected to attract around 60% of all votes. If your client has requested a 99% confidence interval that is no wider than 1% (i.e. 0.01), approximately how many voters will you need to survey?
2. Suppose instead that the candidate of interest is instead expected to attract around 20% of all votes. Would this change the number of voters that you need to survey? If so, by how much?