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 in this shipment. 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 answer in (a) and (b)?
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 in this shipment. 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 answer in (a) and (b)?
Solution Summary: The author explains how to estimate a 95% confidence interval for the population mean of the life of LED bulbs.
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 in this shipment.
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 answer in (a) and (b)?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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