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Ford Peterson
09/15/2023 · Elementary School

A paint manufacturer uses a machine to fill gallon cans with paint ( \( 1 \mathrm{gal}=128 \) 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 128.25 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. Click here to view page 1 of the Standard Normal Table. Click here to view page 2 of the Standard Normal Table. (a) The minimum sample size required to construct a \( 90 \% \) confidence interval is 4 cans. (Round up to the nearest whole number.) (b) The \( 90 \% \) confidence interval for a sample size of 6 is ( \( 128, \square \) ). It mean could be exactly 128 ounces because 128 ounces falls (Round to two decimal places as needed.)

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(a) The minimum sample size required is 4 cans. (b) The 90% confidence interval is (127.71, 128.79). It is possible that the population mean is exactly 128 ounces because it falls within the confidence interval.

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