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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
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Suppose we find that the number of blemishes in 50-foot

Chapter 9, Problem 10E

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QUESTION:

Suppose we find that the number of blemishes in 50-foot tin strips averages about \(\bar{c}=1.4\). Calculate the control limits. Say the process has gone out of control and this average has increased to 3.

(a) What is the probability that the next observation will exceed the UCL?

(b) What is the probability that at least 1 of the next 10 observations will exceed the UCL?

Equation Transcription:

Text Transcription:

Bar c =1.4

Questions & Answers

QUESTION:

Suppose we find that the number of blemishes in 50-foot tin strips averages about \(\bar{c}=1.4\). Calculate the control limits. Say the process has gone out of control and this average has increased to 3.

(a) What is the probability that the next observation will exceed the UCL?

(b) What is the probability that at least 1 of the next 10 observations will exceed the UCL?

Equation Transcription:

Text Transcription:

Bar c =1.4

ANSWER:

Step 1 of 3

The  chart for the number of defectives in a unit has lower and upper control limits given by

and the center line is . When  it is set to zero.

The upper and lower control limits, where

are given by

but the  is set to zero because .

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