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5) Shafts manufactured for use in optical storage devices have diameters that are normally dis- tributed with mean 0.652 cm and standard deviation 0.003 cm. 30 shafts are selected at random from a large lot and measured, and then the sample standard deviation is computed. The specification for the shaft diameter is 0.650 ± 0.004 cm. If the sample standard deviation exceeds 0.004 cm the manufacturing process is reviewed. What is the probability of observing a sample standard deviation greater than 0.004 cm even though the true standard deviation is 0.003 cm? In other words, what is the probability that we are 'unlucky' enough to only select enough 'unacceptable' shafts (and, therefore, conclude there is something wrong with the manufacturing process) when, in fact, the actual standard deviation is acceptable and the process does not need to be reviewed?

5) Shafts manufactured for use in optical storage devices have diameters that are normally dis- tributed with mean 0.652 cm and standard deviation 0.003 cm. 30 shafts are selected at random from a large lot and measured, and then the sample standard deviation is computed. The specification for the shaft diameter is 0.650 ± 0.004 cm. If the sample standard deviation exceeds 0.004 cm the manufacturing process is reviewed. What is the probability of observing a sample standard deviation greater than 0.004 cm even though the true standard deviation is 0.003 cm? In other words, what is the probability that we are 'unlucky' enough to only select enough 'unacceptable' shafts (and, therefore, conclude there is something wrong with the manufacturing process) when, in fact, the actual standard deviation is acceptable and the process does not need to be reviewed?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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5) Shafts manufactured for use in optical storage devices have diameters that are normally dis- tributed with mean 0.652 cm and standard deviation 0.003 cm. 30 shafts are selected at random from a large lot and measured, and then the sample standard deviation is computed. The specification for the shaft diameter is 0.650 ± 0.004 cm. If the sample standard deviation exceeds 0.004 cm the manufacturing process is reviewed. What is the probability of observing a sample standard deviation greater than 0.004 cm even though the true standard deviation is 0.003 cm? In other words, what is the probability that we are 'unlucky' enough to only select enough 'unacceptable' shafts (and, therefore, conclude there is something wrong with the manufacturing process) when, in fact, the actual standard deviation is acceptable and the process does not need to be reviewed?
Transcribed Image Text:5) Shafts manufactured for use in optical storage devices have diameters that are normally dis- tributed with mean 0.652 cm and standard deviation 0.003 cm. 30 shafts are selected at random from a large lot and measured, and then the sample standard deviation is computed. The specification for the shaft diameter is 0.650 ± 0.004 cm. If the sample standard deviation exceeds 0.004 cm the manufacturing process is reviewed. What is the probability of observing a sample standard deviation greater than 0.004 cm even though the true standard deviation is 0.003 cm? In other words, what is the probability that we are 'unlucky' enough to only select enough 'unacceptable' shafts (and, therefore, conclude there is something wrong with the manufacturing process) when, in fact, the actual standard deviation is acceptable and the process does not need to be reviewed?
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