Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let N20 denote the number of parts in the sample of 20 that require rework. a) A process problem is suspected if N20 exceeds its mean by more than three standard deviations. If the percentage of parts that require rework remains at 1%, what is the probability that a process problem is nevertheless suspected? b) If the rework percentage is actually 4%, what is the probability that N20 exceeds 1? c) If the rework percentage is actually 4%, what is the probability that N₂0 exceeds 1 in at least one of the next five hours of samples? d) If the rework percentage is actually 4%, what is the probability that more than two hours of sampling will be required to find the first part which requires rework?
Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let N20 denote the number of parts in the sample of 20 that require rework. a) A process problem is suspected if N20 exceeds its mean by more than three standard deviations. If the percentage of parts that require rework remains at 1%, what is the probability that a process problem is nevertheless suspected? b) If the rework percentage is actually 4%, what is the probability that N20 exceeds 1? c) If the rework percentage is actually 4%, what is the probability that N₂0 exceeds 1 in at least one of the next five hours of samples? d) If the rework percentage is actually 4%, what is the probability that more than two hours of sampling will be required to find the first part which requires rework?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of
the parts require rework. Let N20 denote the number of parts in the sample of 20 that require
rework.
a) A process problem is suspected if N20 exceeds its mean by more than three standard
deviations. If the percentage of parts that require rework remains at 1%, what is the
probability that a process problem is nevertheless suspected?
b) If the rework percentage is actually 4%, what is the probability that N20 exceeds 1?
c) If the rework percentage is actually 4%, what is the probability that N₂0 exceeds 1 in at
least one of the next five hours of samples?
d) If the rework percentage is actually 4%, what is the probability that more than two hours
of sampling will be required to find the first part which requires rework?
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