A factory uses three production lines to manufacture cans of a certain type. The

Question

A factory uses three production lines to manufacture cans of a certain type. The accompanying tabic gives percentages of nonconforming cans, categorized by type of non- conformance, for each of the three lines during a particular lime period. During this period, line 1 produced 500 nonconforming cans, line 2 produced 400 such cans, and line 3 was responsible for 600 nonconforming cans. Suppose that one of these 1500 cans is randomly selected. (a) What is the probability that the can was produced by line 1? That the reason for nonconformance is a crack? (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?

Explanation / Answer

Table with number non-confirming cans:

1500

a)

P(can was produced by line 1) =500/1500 = 1/3 =0.333

P(reason for nonconfermence was a crack) = 666/1500 = 0.444

b)

P(Had blemish given that it came from Line1) = cans with Blemish from Line 1/Total cans from Line 1 = 75/500 =0.15

c)

P(Can came from Line 1 given that it had surface defect) = cans with surface defect from Line 1/Total cans with surface defect = 50/172 =0.29069

Line 1 Line 2 Line 3 Total Blemish 75 48 120 243 Crack 250 176 240 666 Pull-Tab Problem 105 112 144 361 Surface Defect 50 32 90 172 Other 20 32 12 64 Total 500 400 600

1500

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