6. A fraction nonconforming chart has center line p = 0.10, UCL=0.20, and LCL=0.0 a). Assuming a 3-sigma chart is used, what is the sample size for the control chart for p. b). Use the Poisson approximation to the binomial to find the probability of a Type I error a. c). Use the Poisson approximation to find the Type II error if the actual fraction nonconforming = 0.15

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.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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6. A fraction nonconforming chart has center linep = 0.10, UCL=0.20, and LCL=0.0
a). Assuming a 3-sigma chart is used, what is the sample size for the control chart for p.
b). Use the Poisson approximation to the binomial to find the probability of a Type I error a.
c). Use the Poisson approximation to find the Type II error if the actual fraction nonconforming p = 0.15
e). If it is desired that the LCL should not be less than 0.02, what sample size n will guarantee this
value of the LCL. What is the corresponding value for UCL?
Transcribed Image Text:6. A fraction nonconforming chart has center linep = 0.10, UCL=0.20, and LCL=0.0 a). Assuming a 3-sigma chart is used, what is the sample size for the control chart for p. b). Use the Poisson approximation to the binomial to find the probability of a Type I error a. c). Use the Poisson approximation to find the Type II error if the actual fraction nonconforming p = 0.15 e). If it is desired that the LCL should not be less than 0.02, what sample size n will guarantee this value of the LCL. What is the corresponding value for UCL?
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