Question: By law, a manufacturer of a food product must list Food and Drug Administration (FDA) estimates of the contents of the packaged product. Suppose that the FDA needs to estimate the mean sugar content (by weight) in a 16 ounce box of Crunchees corn flakes. The FDA randomly selects 85 boxes of Crunchees corn flakes for testing, and finds that the sugar content of these boxes has a mean of 3.2 ounces and a standard deviation of 0.5 ounce.

(a) (5 points) Assuming that the sugar content is normally distributed, construct a 95% confidence interval for the mean sugar content of 16 ounce boxes of Crunchees corn flakes. Report your answer by completing the sentence "We are 95% confident that . . . ."

(b) (5 points) Explain in plain English what "95% confident" means in this situation.

(c) (5 points) Give one way that the FDA could reduce the width of this confidence interval. What is the drawback to doing this?