s3 az)A factory uses three production lines to manufacture cans of certain type

Question

s3

az)A factory uses three production lines to manufacture cans of certain type the following table awes percentages of confirming cans, categorized by type of nonconformance for each of the three lines during a particular time period conformities Line Line une Blemish Pull Tab problem 21 Surface Detect Tota inspected 500 400 (al suppose that a can selected from this manufacturer what is the probabilty that the can is has a crack given that it was produced by ine-17 (b) the selected can came from line 2. what is the probabil y that it had a blemsh? (cl Given that the selected can had a surface defect, what is the probability that came from line-17 Customer-A states that he does not want to buy cams if the probablity of crack or defect more than 7.5% Can he manufacturer sell the cans for this customer? (Only calculation based answers will get points. el customer B does not want to buy the cans if the probability of crack and blemish percentage is more than 10%. Can the manufacturer sell the cans for this customer? jonly calculation based answers will get points)

Explanation / Answer

You are given the table .

a)

you have to find P( crack given Line 1 )

P( crack given Line1) = number of crack in Line 1 / Total number of inspected in Line 1

= 50 /500

=0.1

b)

P( blemish given Line 2 )=number of blemish in Line 2 / total number of inspected in Line 2

= 12/ 400

=0.03

c)

P( surface defect given Line 1 ) =10/500 =0.02

d)

Probability of crack or defect = 134+33 / 600 =0.2783 = 27.83%

it's more than 7.5 %

So manufacture does not sell the cans for this customer A .

e)

P( crack and blemish ) =P( crack ) * P( blemish )

= 134/600 * 47/600

= 0.0175

= 1.75%

percentage is less than 10 % so manufacturer sell the cans for this customer.

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