## The quality control manager at a light bulb factory needs to

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipm… Show more 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 72 hours. A random sample of 36 light bulbs indicated a sample mean life of 230 hours. Complete parts? (a) through? (d) below. a. Construct a 99?% confidence interval estimate for the population mean life of light bulbs in this shipment.The 99?% confidence interval estimate is from a lower limit of __hours to an upper limit of __hours. ?(Round to one decimal place as? needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 280 ?hours? Explain.Based on the sample? data, the manufacturer __the right to state that the lightbulbs have a mean life of 280 hours. A mean of 280 hours is c. Must you assume that the population light bulb life is normally? distributed? Explain. A. ?Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. B.?No, since ? is known and the sample size is large? enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. C.?Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. D.?No, since ? is? known, the sampling distribution of the mean does not need to be approximately normally distributed. d. Suppose the standard deviation changes to 60 hours. What are your answers in? (a) and? (b)?The 99?% confidence interval estimate would be from a lower limit of __hours to an upper limit of __hours. ?(Round to one decimal place as? needed.) Based on the sample data and a standard deviation of 60 ?hours, the manufacturer ___the right to state that the lightbulbs have a mean life of 280 hours. A mean of 280 hours is ___standard errors ___the sample? mean, so it is ____the lightbulbs have a mean life of 280 hours. • Show less