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 0.7 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 0.80 ounce. ​(b) The sample mean is 128.75 ounces. With a sample size of 6​, a 90​% level of​ confidence, and a population standard deviation of 0.80 ​ounce, does it seem possible that the population mean could be exactly 128 ​ounces? Explain.

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