The operations manager at a light emitting diode (LED) light bulb factory needs to estimate the mean life of a large shipment of LEDs. The manufacturer’s specifications are that the standard deviation is 1,500 hours. A random sample of 64 LEDs indicated a sample mean life of 49,875 hours.

a. Construct a 95% confidence interval estimate for the population mean life of LED light bulbs in this shipment.

b. Do you think that the manufacturer has the right to state that the LED light bulbs have a mean life of 50,000 hours? Explain.

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

d. Suppose that the standard deviation changes to 500 hours. What are your answers in (a) and (b)?