The life of electric lightbulbs is known to be a normally distributed random variable with unknown mean μ and standard deviation 200 hours. The value of a lot of 1,000 bulbs is (1,000) (1/5,000) μ dollars. A random sample of n bulbs is to be drawn by a prospective buyer, and 1,000(1/5,000) X–bar dollars paid to the manufacturer. How large should n be so that the probability is 0.90 that the buyer does not overpay or underpay the manufacturer by more than $15?