7. The quality control manager at a light bulb tactory needs to estimate the mean lite ot a large shipment of light bulbs. The standard deVIation is 75 hours. A random sample of 36 light bulbs indicated a sample mean lite of 250 hours. Complete pans (a) through ((1) below. a. Construct a 95% condence interval estimate tor the population mean life of light bulbs in this shipment. The 95% condence interval estimate is from a lower limit of hours to an upper limit of hours, (Round to one decimal place as needed.) bt Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 300 hours? Explain. Based on the sample data, the manufacturer (1) the right to state that the lightbulbs have a mean lite of 300 hours. A mean of 300 hours is (2) standard errors (3) the sample mean, so it is (4) that the lightbulbs have a mean life of 300 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 at the mean to be approximately normal by the Central Limit Theorem. 0 8. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. 0 C. No, since a is known and the sample size is large enough, the sampling distribution ol the mean is approximately normal by the Central Limit Theorem. 0 D. No, since a is known, the sampling distribution at the mean does not need to be approximately normally distributed. a. Suppose the standard deviation changes to 54 hours. What are your answers in (a) and (b)? The 95% condence 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 54 hours. the manulacturer (5) the right to state that the lighlbulbs have a mean life at 300 hours. A mean of 300 hours is (6) standard errors (7) the sample mean, so it is (8) that the lightbulbs have a mean life of 300 hours. (1) O has (2) 0 less than 2 (3) 0 below (4) O likely (5) 0 does not have (6) 0 less than 2 (7) 0 above (8) 0 highly unlikely 0 does not have 0 4 0 above 0 highly unlikely O has 0 more than5 0 below 0 likely