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-

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