Direct mail advertisers send solicitations (a.k.a. "junk mail") to thousands of potential customers in the hope that some will buy the company's product. The acceptance rate is usually quite low. Suppose a company wants to test the response to a new flyer, and sends it to 1000 people randomly selected from their very large mailing list. They get orders from 123 of the recipients.

a. Construct a 95% confidence interval for the proportion of people the company contacts who may buy something.

b. Determine the sample size necessary to obtain a 95% confidence interval estimate of the proportion of people the company contacts who may buy something if the company wants a margin of error of .02.