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A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, mu, on this subsection among the general population. You decide that you'll use the mean of a random sample of scores on this subsection to estimate mu. . What is the minimum sample size needed in order for you to be 99% confident that your estimate is within 3 of mu? Use the value 20 for the population standard deviation of scores on this subsection.
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).