The lifetime of a certain brand of electric light bulb is known to have a standard deviation of 46 hours. Suppose that a random sample of 50 bulbs of this brand has a mean lifetime of 492 hours. Find a 99% confidence interval for the true mean lifetime of all light bulbs of this brand. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: Upper limit: X S

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