Twenty-five independent polls of one thousand random people each are taken during the course of an extremely close election campaign. People in the poll are asked which of the two candidates they favor and the percentage who favor the incumbent candidate is computed for each poll.

(a)Estimate the standard error and the margin of error for each of these polls. Justify your answer, and briefly explain the difference between them.

(b)How large a poll sample would be required if a margin of error of only 10% was desired?

(c)One of the other candidate's approval ratings averaged around 48% over all the twenty five polls. If you computed the standard deviation of the list of all twenty poll percentages for this candidate, approximately what number would you expect to get? Explain.