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 126 hours. A random sample of 81 light bulbs indicated a sample mean life of 440 hours.

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 412.6 hours to an upper limit of 467.4 hours. - Correct Answer

(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 490

hours? Explain.

Based on the sample data, the manufacturer does not have the right to state that the lightbulbs have a mean life of 490 hours. A mean of 490 hours is more than 3 standard errors above the sample mean, so it is highly unlikely that the lightbulbs have a mean life of 490 hours. Those are the correct answers

c. Must you assume that the population light bulb life is normally distributed? Explain.

No, since is known and the sample size is large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem.- Correct Answer

d. Suppose the standard deviation changes to 108 hours. What are your answers in (a) and (b)?The 95% confidence interval estimate would be from a lower limit of enter your response here hours to an upper limit of enter your response here hours.

(Round to one decimal place as needed.)