The National Weight Control Registry tries to mine secrets of success from people who lost at least 30 pounds and kept it off for at least a year. It reports that out of 2,700 registrants, 459 were on a low-carbohydrate diet (less than 90 grams a day).

a. Develop a 95% confidence interval for the proportion of people on a low-carbohydrate diet. (Round your answers to 3 decimal places.) Answer is complete and correct. b. Is it possible that the population percentage is 18% ? Answer is complete and correct. c. At 95% confidence, how large a sample is needed to estimate the proportion within 0.5% ? (Round up your answer to the next whole number.)