My question is:
A country is about to hold a referendum about joining the European Union. We carry out a survey of a random sample of adult citizens of the country. In the sample, n respondents say that they plan to vote in the referendum. We then ask these respondents whether they plan to vote Yes or No. Define X = 1 if such a person plans to vote Yes, and X = 0 if No.
Suppose that in the whole population 45% of those people who plan to vote are currently planning to vote Yes.
a) Let the sample mean = (Sigma Xi)/ n denote the proportion of the n voters in the sample who plan to vote Yes. What is the central limit theorem approximation of the sampling distribution of the sample mean here?
b) If there are n=50 likely voters in the sample, what is the probability that the sample mean is greater than 0.5?
Any help would be greatly appreciated