Question: A medical researcher proposes o estimate the mean serum cholesterol level of a certain population of middle aged men, based on a random sample of the population. He asks a statistician for advice. The ensuing discussion reveals that the researcher wants to estimate the population mean to within plus or minus 5 mg/dl or less with a 95% confidence. Thus, the standard error of the mean should be 3mg/dl or less. Also, the researcher believes that the standard deviation of serum cholesterol in the population is probably about 40mg/dl. How large a sample does the researcher need to take?