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 bottlingcompany's specifications state that the standard deviation of the amount of water is equal to 0.03 gallon. A random sample of 50 bottles isselected, and the sample mean amount of water per 1-gallon bottle is 0.981 gallon. Complete parts(a) through(d).

a. Construct a 95% confidence interval estimate for the population mean amount of water included in a1-gallon bottle.

0.97268

0.97268

0.98932

0.98932

(Round to five decimal places asneeded.)

b. On the basis of theseresults, do you think that the distributor has a right to complain to the water bottlingcompany? Why?

Yes,

because a1-gallon bottle containing exactly1-gallon of water lies outside

the 95% confidence interval.

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

A.

Yes, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In thiscase, the value of n is small.

B.

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

C.

No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In thiscase, the value of n is large.

Your answer is correct.

D.

No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is small. In thiscase, the value of n is small.

d. Construct a 90% confidence interval estimate. How does this change your answer to part(b)?

(Round to five decimal places asneeded.)