A paint manufacturer uses a machine to fill gallon cans with paint (see figure). 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 0.75 ounce.

(b) The sample mean is 127.75 ounces. With a sample size of 8, a 90% level of confidence, and a population standard deviation of 0.75 ounce, does it seem possible that the population mean could be exactly 128 ounces? Explain.

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Error tolerance = 0.5 oz terior Latex Paint White 1 gallon Volume = 1 gal (128 oz)