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 85 , what is the minimum sample size needed for the psychologist to be 95% confident that her estimate is within 12 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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