A cheese processing company wants to estimate the mean cholesterol content of all​ one-ounce servings of a type of cheese. The estimate must be within 0.75 milligram of the population mean. ​(a) Determine the minimum sample size required to construct a 95​% confidence interval for the population mean. Assume the population standard deviation is 3.07 milligrams. ​(b) The sample mean is 26 milligrams. Using the minimum sample size with a 95​% level of​ confidence, does it seem likely that the population mean could be within 3​% of the sample​ mean? within 0.3​% of the sample​ mean? Explain.

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