What is the probability that a candidate will be forecast as the winner when the population…

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, then that candidate will be forecast as the winner of the election.

If a random sample of 100 voters is selected, what is the probability that a candidate will be forecast as the winner when

a.

the true percentage of her vote is 50.1%?

b.

the true percentage of her vote is 60%?

c.

the true percentage of her vote is 49% (and she will actually lose the election)?

d.

Find a 95% confidence interval of the true percentage of her vote, if 55 voters in the sample of 100 indicated that they voted for her. Can we be sure that she has won the election?

e.

If 55% of a sample of 300 indicated that they have voted for her, is there sufficient evidence at 90% level of confidence that she has won the election? (Hint: If 0.5 or less is within the C.I., then no.)