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Samples of 20 parts from a metal punching process are
Chapter 3, Problem 108E(choose chapter or problem)
Problem 108E
Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 20 that require rework. A process problem is suspected if X exceeds its mean by more than 3 standard deviations.
(a) If the percentage of parts that require rework remains at 1%, what is the probability that Xexceeds its mean by more than 3 standard deviations?
(b) If the rework percentage increases to 4%, what is the probability that X exceeds 1?
(c) If the rework percentage increases to 4%, what is the probability that X exceeds 1 in at least one of the next five hours of samples?
Questions & Answers
QUESTION:
Problem 108E
Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 20 that require rework. A process problem is suspected if X exceeds its mean by more than 3 standard deviations.
(a) If the percentage of parts that require rework remains at 1%, what is the probability that Xexceeds its mean by more than 3 standard deviations?
(b) If the rework percentage increases to 4%, what is the probability that X exceeds 1?
(c) If the rework percentage increases to 4%, what is the probability that X exceeds 1 in at least one of the next five hours of samples?
ANSWER:
Solution:
Step 1 of 4:
Let X follows the Binomial distribution with the probability mass function
P(X = x) =
Where, n = 20, p = 0.01 (1%), and q = 0.99
Mean = np
= 20(0.01)
= 0.2
Standard deviation =
=
= 0.445.