statistics q47

A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, u, 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 u. What is the minimum sample size needed in order for you to be 99% confident that your estimate is within 2 of u? Use the value 22 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.) X