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 0.04 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.952 gallon.

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?

Yes or No because a 1-gallon bottle containing exactly 1-gallon of water lies outside or within the 95% confidence interval.

c. Must you assume that the population amount of water per bottle is normally distributed here? Explain.

1. 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.
2. 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.
3. 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.
4. 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)?

_____ nothing

(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 outside or within the 90% confidence interval. The distributor: still has, now has, now does not have, still does not have, a right to complain to the bottling company.