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 be95

%

confident that your estimate is within3

of

? Use the value23

for the population standard deviation of scores on this subsection.

Carry your intermediate computations to at least three decimal places.