Question

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 92 hours. A random sample of 64 light bulbs indicated a sample mean life of 360 hours. Complete parts (a) through (d) below. that the lightbulbs have a mean life of 410 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. O C. No, since o is known and the sample size is large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. OD. 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 76 hours. What are your answers in (a) and (b)? The 99% confidence interval estimate would be from a lower limit of (Round to one decimal place as needed.) hours to an upper limit of hours. the right to state that the lightbulbs have a mean life of 410 hours. A mean of 410 hours is standard errors Based on the sample data and a standard deviation of 76 hours, the manufacturer the sample mean, so it is that the lightbulbs have a mean life of 410 hours.