Question

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. Blemish Crack Pull-Tab Problem Surface Defect Other Line 1 Line 2 15 12 50 44 21 28 10 8 4 3 Line 3 20 40 24 15 2 During this period, line i produced 300 nonconforming cans, line 2 produced 800 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.)

Answer 1

Given information Line I line 2 Total line 3 20 Blemish 47 Cyack pull tab problem Surface defect other Total 100 100 101 301 » production production production of of of line - 300 line 2 - 800 line 3 » 200 Total d 1300. production - 300+800+200 a) i) The produced by line I is probability that the can 300 - 10.23076 300 1300 is a crack i) probability that the reason for nonconformance .. P(crack) - 500 (300) + 44 (890) + 40 (200) 1300 -10.444 6) probability that of blemish from line 1 581.2017 1300 c) probability of surface detect from line 1 ip (Surface detet) O (500) + 1.(800) + 16. (200) » di » 0.93 2 133

Now Pl line if surface detect) 0.10(300) 1300 30 => 0.02307 1300 Now pltime of surface detect) » p(surfacedtect) 0.02307 0.932 0.02307 0.932 0.02475

done best to my knowledge. feel free to comment if you have any doubt.

ur thump up helps me alot. thank you