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 0.03 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.997 gallon. Complete parts (a) through (d). a. Construct a 95% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle. (Round to five decimal places as needed.) b. On the basis of these results, do you think that the distributor has a right to complain to the water bottling company? Why? because a 1-gallon bottle containing exactly 1-gallon of water lies the 95% confidence interval. c. Must you assume that the population amount of water per bottle is normally distributed here? Explain. A. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. O B. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is large C. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is small. In this case, the value of n is small. O D. Yes, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is small. d. Construct a 90% confidence interval estimate. How does this change your answer to part (b)? SHS (Round to five decimal places as needed.) How does this change your answer to part (b)? A 1-gallon bottle containing exactly 1-gallon of water lies the 90% confidence interval. The distributor right to complain to the bottling company