The operations manager at a compact fluorescent light bulb (CFL) factory needs to estimate the mean life of a large shipment of CFLs. The manufacturer’s specifications are that the population standard deviation is 1,000 hours. A random sample of 64 CFLs indicated a sample mean life of 7,500 hours.

Construct a 95% confidence interval estimate for the popu- lation mean life of compact fluorescent light bulbs in this shipment.

The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 7500 - 245 = 7255 hours.

The upper end of the interval is the sample mean added to M. So it is 7500 + 245 = 7745 hours.

The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.

98%

step-by-step explanation:

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