7.14 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 actu-ally lose the election)?

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