Please help with last answer

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 98 hours. A random sample of 49 light bulbs indicated a sample mean life of 360 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

323.8

323.8 hours to an upper limit of

396.1

396.1 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 410 hours? Explain.

Based on the sampledata, the manufacturer does not have

the right to state that the lightbulbs have a mean life of 410 hours. A mean of 410 hours is more than 3

standard errors above

the samplemean, so it is highly unlikely

that the lightbulbs have a mean life of 410 hours.

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

A.

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

Your answer is correct.

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 isknown, the sampling distribution of the mean does not need to be approximately normally distributed.

D.

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

d. Suppose the standard deviation changes to 84 hours. What are your answers in(a) and(b)?

The 99% confidence interval estimate would be from a lower limit of

329.1

329.1 hours to an upper limit of

390.9

390.9 hours.

(Round to one decimal place asneeded.)

Based on the sample data and a standard deviation of 84 hours, the manufacturer

the right to state that the lightbulbs have a mean life of 410 hours. A mean of 410 hours is

standard errors

the samplemean, so it is

that the lightbulbs have a mean life of 410 hours.