Concept explainers
Consider a 3-sigma control chart with a center line at µ0 and based on n = 5. Assuming normality, calculate the
a. µ0 + .5σ
b. µ0 − σ
c. µ0 + 2σ
a.
Find the probability that a single point will fall outside the control limits when the actual process mean is
Answer to Problem 7E
The probability that a single point will fall outside the control limits when the actual process mean is
Explanation of Solution
Given info:
Consider, a 3-sigma control chart based on center line
Calculation:
It is known that for a 3-sigma chart the probability that a single point will fall outside the control limits when the actual process mean is
It is known that, for a random variable X that follows normal distribution with mean
Thus,
Now, for
According to table A.3, “Standard Normal Curve Areas” of Appendix the standard normal variable value for
Thus,
Thus, the probability that a single point will fall outside the control limits when the actual process mean is
b.
Find the probability that a single point will fall outside the control limits when the actual process mean is
Answer to Problem 7E
The probability that a single point will fall outside the control limits when the actual process mean is
Explanation of Solution
Calculation:
It is known that for a 3-sigma chart the probability that a single point will fall outside the control limits when the actual process mean is
It is known that, for a random variable X that follows normal distribution with mean
Thus,
Now, for
According to table A.3, “Standard Normal Curve Areas” of Appendix the standard normal variable value for
Thus,
Thus, the probability that a single point will fall outside the control limits when the actual process mean is
c.
Find the probability that a single point will fall outside the control limits when the actual process mean is
Answer to Problem 7E
The probability that a single point will fall outside the control limits when the actual process mean is
Explanation of Solution
Calculation:
It is known that for a 3-sigma chart the probability that a single point will fall outside the control limits when the actual process mean is
It is known that, for a random variable X that follows normal distribution with mean
Thus,
Now, for
According to table A.3, “Standard Normal Curve Areas” of Appendix the standard normal variable value for
Thus,
Thus, the probability that a single point will fall outside the control limits when the actual process mean is
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Chapter 16 Solutions
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- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill