A paint manufacturer uses a machine to fill gallon cans with paint​ (1 gal=128 ​ounces). The manufacturer wants to estimate the mean volume of paint the machine is putting in the cans within 0.5 ounce. Assume the population of volumes is normally distributed. ​(a) Determine the minimum sample size required to construct a 90​% confidence interval for the population mean. Assume the population standard deviation is 0.79 ounce. ​(b) The sample mean is 128.25 ounces. With a sample size of 8​, a 90​% level of​ confidence, and a population standard deviation of 0.79 ​ounce, does it seem possible that the population mean could be exactly 128 ​ounces? Explain.

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A paint manufacturer uses a machine to fill gallon cans with paint​ (1
gal=128
​ounces). The manufacturer wants to estimate the mean volume of paint the machine is putting in the cans within
0.5
ounce. Assume the population of volumes is normally distributed.
​(a) Determine the minimum sample size required to construct a
90​%
confidence interval for the population mean. Assume the population standard deviation is
0.79
ounce.
​(b) The sample mean is
128.25
ounces. With a sample size of
8​,
a
90​%
level of​ confidence, and a population standard deviation of
0.79
​ounce, does it seem possible that the population mean could be exactly
128
​ounces? Explain.
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