Suppose 55% of the people in a city with a population of 300,000 favor candidate A, while 45% favor candidate B. A random sample of 150 people is chosen without replacement from this city.

(a) Find an exact expression for the probability that at least 54% of the people in the sample favor candidate A. Use summation notation for your answer. Evaluate your answer. Write down your answer in decimal form to the nearest 5 decimal places.

(b) Estimate the answer to (a) using a binomial approximation. Again write your answer in summation notation.

(c) Estimate the answer to (b) using a normal approximation with the continuity correction.