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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 0.961 gallon. Complete pa (a) through (d). a. Construct a 99% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle. SHS (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 99% confidence interval, c. Must you assume that the population amount of water per bottle is normally distributed here? Explain. O A. 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. B. 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. O 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, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. d. Construct a 90% confidence interval estimate. How does this change your answer to part (b)? SUS (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 a right to complain to the bottling company