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 84 hours. A random sample of 49 light bulbs indicated a sample mean life of 310 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 asneeded.)

b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 360 hours? Explain.

Based on the sampledata, the manufacturer has or does not have the right to state that the lightbulbs have a mean life of 360 hours.

A mean of 360 hours is ( less than 2 or more than 4) standard errors ( above or below) the samplemean, so it is ( likely highly or unlikely ) that the lightbulbs have a mean life of 360 hours.

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

A.Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.

B.Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.

C.No, since is known and the sample size is largeenough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem.

D.No, since isknown, the sampling distribution of the mean does not need to be approximately normally distributed.

d. Suppose the standard deviation changes to 63 hours. What are your answers in(a) and(b)?

The 95% confidence interval estimate would be from a lower limit of

nothing

hours to an upper limit of _____ hours.

(Round to one decimal place asneeded.)

Based on the sample data and a standard deviation of 63 hours, the manufacturer ( has or does not have) the right to state that the lightbulbs have a mean life of 360 hours. A mean of 360 hours is ( more than 5 or less than 2

standard errors ( below or above) the samplemean, so it is ( highly unlikely or likely) that the lightbulbs have a mean life of 360 hours.