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...

A paint manufacturer uses a machine to fill gallon cans with paint​ (1

​ounces). The manufacturer wants to estimate the mean volume of paint the machine is putting in the cans within

ounce. Assume the population of volumes is normally distributed.

​(a) Determine the minimum sample size required to construct a

confidence interval for the population mean. Assume the population standard deviation is

ounce.

​(b) The sample mean is

ounces. With a sample size of

a

level of​ confidence, and a population standard deviation of

​ounce, does it seem possible that the population mean could be exactly

​ounces? Explain.