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 ofwater contained in
1​-gallon
bottles purchased from a nationally known water bottlingcompany. The water bottling​ company's specifications statethat 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 waterper
1​-gallon
bottle is
0.971
gallon. Complete parts​ (a) through​ (d).
Question content area bottom
Part 1
a.
Construct a
95​%
confidence interval estimate for the population mean amount ofwater 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 thedistributor has a right to complain to the waterbottling​ company? Why?
▼
Yes,
No,
because a​ 1-gallon bottle containingexactly​ 1-gallon of water lies
▼
within
outside
the
95​%
confidence interval.
Part 3
c.
Must you assume that the population amount of water per bottleis normally distributed​ here? Explain.
A.​No, because the Central Limit Theorem almost always ensuresthat
X
is normally distributed when n is small. In this​ case, thevalue of n is small.
B.​Yes, because the Central Limit Theorem almost always ensuresthat
X
is normally distributed when n is large. In this​ case, thevalue of n is small.
C.
​Yes, since nothing is known about the distribution ofthe​ population, it must be assumed that the population isnormally distributed.
D.​No, because the Central Limit Theorem almost always ensuresthat
X
is normally distributed when n is large. In this​ case, thevalue of n is large.
Part 4
d.
Construct a
90​%
confidence interval estimate. How does this change your answerto part​ (b)?
enter your response here≤μ≤enter your response here
​(Round to five decimal places as​ needed.)
Part 5
How does this change your answer to part​ (b)?
A​ 1-gallon bottle containing exactly​ 1-gallon ofwater lies
▼
outside
within
the
90​%
confidence interval. The distributor
▼
still has
still does not have
now has
now does not have
a right to complain to the bottling company.