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Quality control (2.2, 5.3, 6.3) Many manufactur- ing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the pro- duction shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean 4, with a standard deviation of o. For each question that follows, assume that the process is working properly. (a) What's the probability that at least one of the next two sample means will fall more than 20 from the target mean u? Show your work. (b) What's the probability that the first sample mean that is greater than u + 2o is the one from the fourth sample taken? (c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the 5 most recent sample means. If at least 4 of the 5 fall outside the interval (u – o, p+ o), they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.

Quality control (2.2, 5.3, 6.3) Many manufactur- ing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the pro- duction shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean 4, with a standard deviation of o. For each question that follows, assume that the process is working properly. (a) What's the probability that at least one of the next two sample means will fall more than 20 from the target mean u? Show your work. (b) What's the probability that the first sample mean that is greater than u + 2o is the one from the fourth sample taken? (c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the 5 most recent sample means. If at least 4 of the 5 fall outside the interval (u – o, p+ o), they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.

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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Quality control (2.2, 5.3, 6.3) Many manufactur- ing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the pro- duction shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean 4, with a standard deviation of o. For each question that follows, assume that the process is working properly. (a) What's the probability that at least one of the next two sample means will fall more than 20 from the target mean u? Show your work. (b) What's the probability that the first sample mean that is greater than u + 2o is the one from the fourth sample taken? (c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the 5 most recent sample means. If at least 4 of the 5 fall outside the interval (u – o, p+ o), they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.
Transcribed Image Text:Quality control (2.2, 5.3, 6.3) Many manufactur- ing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the pro- duction shift. Assuming that the process is working properly, the mean measurements from these random samples will vary Normally around the target mean 4, with a standard deviation of o. For each question that follows, assume that the process is working properly. (a) What's the probability that at least one of the next two sample means will fall more than 20 from the target mean u? Show your work. (b) What's the probability that the first sample mean that is greater than u + 2o is the one from the fourth sample taken? (c) Plant managers are trying to develop a criterion for determining when the process is not working properly. One idea they have is to look at the 5 most recent sample means. If at least 4 of the 5 fall outside the interval (u – o, p+ o), they will conclude that the process isn't working. Is this a reasonable criterion? Justify your answer with an appropriate probability.
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