Question

A bottled water distributor wants to estimate the amount of water contained in 11​-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 0.040.04 gallon. A random sample of 5050 bottles is​ selected, and the sample mean amount of water per 11​-gallon bottle is 0.992 gallon. COMPLETE PARTS (a) THROUGH (d).

a. Construct a 99​% 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?

NO OR YES, because a​ 1-gallon bottle containing exactly​ 1-gallon of water lies OUTSIDE OR WITHIN the 99​% confidence interval.

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

A.​Yes, because the Central Limit Theorem almost always ensures that Upper X overbarX is normally distributed when n is large. In this​ case, the value of n is small.

B. ​Yes, since nothing is known about the distribution of the​ population, it must be assumed that the population is normally distributed.

C.​No, because the Central Limit Theorem almost always ensures that Upper X overbarX is normally distributed when n is large. In this​ case, the value of n is large.

D.​No, because the Central Limit Theorem almost always ensures that Upper X overbarX is normally distributed when n is small. In this​ case, the value of n is small.

d. Construct a 95​% confidence interval estimate. How does this change your answer to part​ (b)?

​(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 lie OUTSIDE OR WITHIN the 95​% confidence interval. The distributor NOW HAS OR NOW DOES NOT HAVE OR STILL DOES NOT HAVE OR STILL HAS a right to complain to the bottling company.

Answer 1

hey it seems that there is a typo in your question.

A bottled water distributor wants to estimate the amount of water contained in 11​-gallon bottles purchased from a nationally known water bottling company.   Here it should be 1-gallon I guess.

question is based on large sample theory.

so assuming that the answer is as follows-