A food company is planning to market a new kind of cereal; however, before marketing this product, the company wants to find the percentage of people who will like it. The company’s research department selected a random sample of 500 persons and asked them to taste the cereal. Of these 500 people, 290 said they liked it. 

a. Compute the 95% confidence interval for the percentage of the population that will like the cereal.
b. Interpret this confidence interval.
c. How many people should be selected in order to be 99% confident of being within 1% of the population percentage of people who will like the cereal?