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 3.10 milligrams. 

(b) The sample mean is 29 milligrams. Using the minimum sample size with a 95% level of confidence, does it seem possible that the population mean could be within 3% of the sample mean? within 0.3% of the sample mean? Explain.