A psychologist is studying self image of smokers, which she measures by the self image score from a personality inventory. She would like to estimate the mean self image score, u, for the population of all smokers. She plans to take a random sample of self image scores for smokers and estimate u via this sample. Assuming that the standard deviation of self image scores for the population of all smokers is 85, what is the minimum sample size needed for the psychologist to be 95% confident that their estimate is within 10 of u?

Carry your intermediate computations to at least 3 decimal places.

Write your answer as a whole number ( and make sure that it is the minimum whole number that satisfies the requirements)