Question: The quality control manager at a light-bulb factory needs to estimate the mean life of a large shipment of light-bulbs. The process standard deviation is known to be 100 hours. A random sample of 64 light-bulbs indicated a sample mean life of 350 hours.

1. Set up a 95% confidence intervals estimate of the true population mean life of light-bulbs in this shipment.
2. Do you think the manufacturer has the right to state that the light-bulbs last an average of 400 hours?
3. Does the population of light-bulbs life have to be normally distributed here?
4. Explain why an observed value of 320 hours for a single light-bulb is not unusual, even though it is outside the confidence interval you have calculated.

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