A psychologist is studying the self-image ofsmokers, which s

A psychologist is studying the self-image ofsmokers, which she measures by the selfimage (SI) score from a personalityinventory.  She would like to estimatethe mean SI score µ for the population of all smokers.  She plans to take a random sample of SIscores for smokers and estimate µ via this sample.  Assuming that the standard deviation of SIscores of the population of all smokers is 85, what is the minimum sample sizeneeded for the psychologist to be 99% confident that her estimate is within 15of µ?