A city is planning to build a hydroelectric power plant. A local newspaper found that 53% of the voters in this city favor the construction of this plant. Assume that this result holds true for the population of all voters in this city.
a. What is the probability that more than 50% of the voters in a random sample of 200 voters selected from this city will favor the construction of this plant?
b. A politician would like to take a random sample of voters in which more than 50% would favor the plant construction. How large a sample should be selected so that the politician is 95% sure of this outcome?