A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. The water bottling company's specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon.
a. Construct a 99% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle.
b. On the basis of these results, do you think that the distributor has a right to complain to the water bottling company? Why?
c. Must you assume that the population amount of water per bottle is normally distributed here? Explain.
d. Construct a 95% confidence interval estimate. How does this change your answer to (b)?