Chapter 7, Problem 14PS

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least $55\%$ of the vote in the sample, that candidate will be forecast as the winner of the election , if you select a random sample of 100 voters, what is the probability that a candidate will be forecast as the winner when

a. the population percentage of her vote is $50.1\%?$

b. the population percentage of her vote is $60\%?$

c. the population percentage of her vote is $49\%$ (and she will actually lose the election)?

d. If the sample size is increased to 400, what are your answer to (a) through (c)? Discuss.