A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you are interested in the mean score, mu, on this subsection among the general population. You decide that you will 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 2 of mu? 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).