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

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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 0.01 gallon. A random sample of 50 bottles is​
selected, and the sample mean amount of water per 1​-gallon bottle
is 0.997 gallon. Complete parts​ (a) through​ (d).
Part 1 a. Construct a 95​% confidence interval estimate for the
population mean amount of water included in a​ 1-gallon bottle.
enter your response here≤μ≤enter your response here ​(Round to five
decimal places as​ needed.)
Part 2 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, Yes, because a​ 1-gallon bottle containing exactly​
1-gallon of water lies ▼ within outside the 95​% confidence
interval.
Part 3 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 X is normally distributed when n is large. In this​
case, the value of n is small.
B. ​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.
C. ​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.
D. ​Yes, since nothing is known about the distribution of the​
population, it must be assumed that the population is normally
distributed.