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 108 hours. A random sample of 64 light bulbs indicated a sample mean life of 370 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 **335.2** hours to an upper limit of **404.8** 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 430 hours? Explain.**Based on the sample data, the manufacturer **does not have** the right to state that the lightbulbs have a mean life of 430 hours. A mean of 430 hours is **more than 4** standard errors **above** the sample mean, so it is **highly unlikely** that the lightbulbs have a mean life of 430 hours.**c. Must you assume that the population light bulb life is normally distributed? Explain.**- A. No, since σ is known, the sampling distribution of the mean does not need to be approximately normally distributed.- B. No, since σ 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. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.**d. Suppose the standard deviation changes to 88 hours. What are your answers in (a) and (b)?**The 99% confidence interval estimate would be from a lower limit of **347.4** hours to an upper limit of **392.6** hours. (Round to one decimal place as needed.)Based on the sample data and a standard deviation of 88 hours, the manufacturer **does not have** the right to state that the lightbulbs have a mean life of 430 hours. A mean of 430 hours is **more than 5** standard errors **above** the sample mean, so it is **highly

Given information Sample size(n) = 64 Sample mean x̅ = 370 Population standard deviation = 88…

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 108 hours. A random sample of 64 light bulbs indicated a sample mean life of 370 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 335.2 hours to an upper limit of 404.8 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 430 hours? Explain. Based on the sample data, the manufacturer does not have the right to state that the lightbulbs have a mean life of 430 hours. A mean of 430 hours is more than 4 standard errors above the sample mean, so it is highly unlikely that the lightbulbs have a mean life of 430 hours. above c. Must you assume that the population light bulb life is normally distributed? Explain. O A. No, since o is known, the sampling distribution of the mean does not need to be approximately normally distributed. O B. No, since a is known and the sample size is large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. O c. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O D. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. d. Suppose the standard deviation changes to 88 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 88 hours, the manufacturer v the right to state that the lightbulbs have a mean life of 430 hours. A mean of 430 hours is v standard errors V the sample mean, so it is V that the lightbulbs have a mean life of 430 hours.