A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, μ, 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 μ. What is the minimum sample size needed in order for you to be 95% confident that your estimate is within 3 of μ ? Use the value 23 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).
(If necessary, consult a list of formulas.)