The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 84 hours. A random sample of 49 light bulbs indicated a sample mean life of 270 hours. Complete parts​ (a) through​ (d) below. a. Construct a 95​% confidence interval estimate for the population mean life of light bulbs in this shipment. The 95​% confidence interval estimate is from a lower limit of nothing hours to an upper limit of nothing hours. ​(Round to one decimal place as​ needed.)

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