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 Me of 280 hours Complete parts (a) through (d) below a Construct a 96% confidence interval estimate for the population mean Me of light bulbs in this shipment The 95% 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 ife of 330 hours? Explain Based on the sample data, the manufacturer 50 tis the right to state that the lightbulbs have a mean life of 330 hours A mean of 330 hours is standard onors the sample mean that the lightbulbs have a mean lide of 330 hours e. Must you assume that the population light bulbi life is normally distributed? Explain OA Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem OB. Yes, the sample size is too large for the samping distribution of the mean to be approximately normal by the Central Limit Theorem OC. No, since e is known, the sampling distribution of the mean does not need to be approximately normally distributed OD. No, since a is known and the sample size is large enough, the sampling darbution of the mean is approximately normal by the Central Land Theorem d. Suppose the standard deviation changes to 70 hours What are your answers in (a) and (b The 96% confidence interval estimate would be (Round to one decimal place as needed) na lower smit of hours to an upper limit of hours Based on the sample data and a standard dovuton of 70 hours, the manufacturer the night to state that the lightbulbs have a mean she of 330 hours A mean of 330 hours n standard enors the sample mean so that the lightbulbs have a mean ife of 330 hours