In political polling, randomly selected voters are asked whether they would vote for a particular candidate A random variable 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 has a Bernoulli distribution The variance of the Bernoulli distribution is known to be(1) p ( 1 p ) where () 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 Suppose you have been commissioned to conduct a poll to determine the popularity of a candidate who is expected to attract around 50 of all votes If your client has requested a 90 confidence interval that is no wider than 1 (i e 0 01), approximately how many voters will you need to survey Suppose instead that the candidate of interest is expected to attract around 10 of all votes Would this change the number of voters that you need to survey If so, by how much

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

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

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

(

)

where=()

(

)

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.Suppose you have been commissioned to conduct a poll to determine the popularity of a candidate who is expected to attract around 50% of all votes. If your client has requested a 90% confidence interval that is no wider than 1% (i.e. 0.01), approximately how many voters will you need to survey?
Suppose instead that the candidate of interest is expected to attract around 10% of all votes. Would this change the number of voters that you need to survey? If so, by how much?