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 specications 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 1gallon bottle is 0.973 gallon. Complete parts (a) through (d). a. Construct a 99% condence interval estimate for the population mean amount of water included in a 1-gallon bottle. | S u S | (Round to ve 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? lV because a 1-gallon bottle containing exactly 1-gallon of water lies V the 99% condence 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 )_( is normally distributed when n is large. In this case, the value of n is large. 0 B- No, because the Central Limit Theorem almost always ensures that )_( is normally distributed when n is small. In this case, the value of n is small. 0 (3- Yes, because the Central Limit Theorem almost always ensures that )_( is normally distributed when n is large. In this case, the value of n is small. 0 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% condence interval estimate. How does this change your answer to part (b)? ISuSI In,......,l h. 3:...t AAA...\" \"hum- A- -nhan.' \\