A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score,

A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you're interested in the mean score, ?, 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 ?. What is the minimum sample size needed in order for you to be 95% confident that your estimate is within 4 of ?? 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).

(If necessary, consult a list of formulas.)