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

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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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