A psychologist is studying the self image of smokers, which she measures by the self-image (SI) score from a personality inventory. She would like to estimate the mean SI score,  μ , for the population of all smokers. She plans to take a random sample of SI scores for smokers and estimate  μ  via this sample. Assuming that the standard deviation of SI scores for the population of all smokers is  80 , what is the minimum sample size needed for the psychologist to be  95%  confident that her estimate is within  15  of  μ ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).

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