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...

Extracted text: 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 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 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 V the right to state that the lightbulbs have a mean life of 280 hours. A mean of 280 hours is V standard errors the sample mean, so it is that the lightbulbs have a mean life of 280 hours. c. Must you assume that the population light bulb life is normally distributed? Explain. O 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. O B. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. OC. No, since o is known and the sample size is large enough, the sampling distribution of the mean approximately normal by the Central Limit Theorem. O D. No, since o is known, the sampling distribution of the mean does not need to be approximately normally distributed. d. Suppose the standard deviation changes to 51 hours. What are your answers in (a) and (b)? The 95% 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 51 hours, the manufacturer v 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 that the lightbulbs have a mean life of 280 hours.