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4. The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of u = 1000 µF and a standard deviation of 80 µF. A sample of 16 capacitors is taken and the average of the capacitances values is computed. Based from the manufacturer's standards, the machine is working properly if the computed average capacitance falls within 950 µF and 1050 µF. Otherwise, we conclude that µ # 1000 µF. A. Determine the probability of committing a type I error when u = 1000 µF. B. Determine the probability of committing a type II error when u = 1080 uF. Hint: Use the sampling distribution of the mean when computing the probabilities.

4. The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of u = 1000 µF and a standard deviation of 80 µF. A sample of 16 capacitors is taken and the average of the capacitances values is computed. Based from the manufacturer's standards, the machine is working properly if the computed average capacitance falls within 950 µF and 1050 µF. Otherwise, we conclude that µ # 1000 µF. A. Determine the probability of committing a type I error when u = 1000 µF. B. Determine the probability of committing a type II error when u = 1080 uF. Hint: Use the sampling distribution of the mean when computing the probabilities.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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4. The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of u = 1000 µF and a standard deviation of 80 µF. A sample of 16 capacitors is taken and the average of the capacitances values is computed. Based from the manufacturer's standards, the machine is working properly if the computed average capacitance falls within 950 µF and 1050 µF. Otherwise, we conclude that µ # 1000 µF. A. Determine the probability of committing a type I error when u = 1000 µF. B. Determine the probability of committing a type II error when u = 1080 uF. Hint: Use the sampling distribution of the mean when computing the probabilities.
Transcribed Image Text:4. The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of u = 1000 µF and a standard deviation of 80 µF. A sample of 16 capacitors is taken and the average of the capacitances values is computed. Based from the manufacturer's standards, the machine is working properly if the computed average capacitance falls within 950 µF and 1050 µF. Otherwise, we conclude that µ # 1000 µF. A. Determine the probability of committing a type I error when u = 1000 µF. B. Determine the probability of committing a type II error when u = 1080 uF. Hint: Use the sampling distribution of the mean when computing the probabilities.
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