A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationa

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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 0.03 gallon. A random sample of 50 bottles is
selected, and the sample mean amount of water per 1-gallon bottle
is 0.993 gallon.
a. Construct a 99% confidence interval estimate for the
population mean amount of water included in a 1-gallon bottle.
b. On the basis of these results, do you think that the
distributor has a right to complain to the water bottling company?
Why?
c. Must you assume that the population amount of water per
bottle is normally distributed here? Explain.
d. Construct a 95% confidence interval estimate. How does this
change your answer to (b)?