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A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three lines during a particular time period. Line 1 Line 2 Line 3 Blemish 15 12 20 Crack 50 44 40 Pull-Tab Problem Surface Defect Other 21 28 24 10 4 8 8 15 1 During this period, line 1 produced 500 nonconforming cans, line 2 produced 600 such cans, and line 3 was responsible for 200 nonconforming cans. Suppose that one of these 1,300 cans is randomly selected. (a) What is the probability that the can was produced by line 1? (Round your answer to three decimal places.) What is the probability that the reason for nonconformance is a crack? (Round your answer to three decimal places.) (b) If the selected can came from line 1, what is the probability that it had a blemish? (c) Given that the selected can had a surface defect, what is the probability that it came from line 1? (Round your answer to three decimal places.)

A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three lines during a particular time period. Line 1 Line 2 Line 3 Blemish 15 12 20 Crack 50 44 40 Pull-Tab Problem Surface Defect Other 21 28 24 10 4 8 8 15 1 During this period, line 1 produced 500 nonconforming cans, line 2 produced 600 such cans, and line 3 was responsible for 200 nonconforming cans. Suppose that one of these 1,300 cans is randomly selected. (a) What is the probability that the can was produced by line 1? (Round your answer to three decimal places.) What is the probability that the reason for nonconformance is a crack? (Round your answer to three decimal places.) (b) If the selected can came from line 1, what is the probability that it had a blemish? (c) Given that the selected can had a surface defect, what is the probability that it came from line 1? (Round your answer to three decimal places.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three lines during a particular time period. Line 1 Line 2 Line 3 Blemish 15 12 20 Crack 50 44 40 Pull-Tab Problem Surface Defect Other 21 28 24 10 4 8 8 15 1 During this period, line 1 produced 500 nonconforming cans, line 2 produced 600 such cans, and line 3 was responsible for 200 nonconforming cans. Suppose that one of these 1,300 cans is randomly selected. (a) What is the probability that the can was produced by line 1? (Round your answer to three decimal places.) What is the probability that the reason for nonconformance is a crack? (Round your answer to three decimal places.) (b) If the selected can came from line 1, what is the probability that it had a blemish? (c) Given that the selected can had a surface defect, what is the probability that it came from line 1? (Round your answer to three decimal places.)
Transcribed Image Text:A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three lines during a particular time period. Line 1 Line 2 Line 3 Blemish 15 12 20 Crack 50 44 40 Pull-Tab Problem Surface Defect Other 21 28 24 10 4 8 8 15 1 During this period, line 1 produced 500 nonconforming cans, line 2 produced 600 such cans, and line 3 was responsible for 200 nonconforming cans. Suppose that one of these 1,300 cans is randomly selected. (a) What is the probability that the can was produced by line 1? (Round your answer to three decimal places.) What is the probability that the reason for nonconformance is a crack? (Round your answer to three decimal places.) (b) If the selected can came from line 1, what is the probability that it had a blemish? (c) Given that the selected can had a surface defect, what is the probability that it came from line 1? (Round your answer to three decimal places.)
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