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 95% confident that your estimate is within 4 of u?

Use the value 22 for the population standard deviation of scores on this subsection.

Carry your intermediate computations to at least 3 decimal places.

Write your answer as a whole number making sure it is the minimum.