SOLUTION: Sales A manufacturer makes two models of an item: model I, which accounts for 80% of unit sales, and model II, which accounts for 20% of unit sales. Because of defects, the manufac
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Question 1169237: Sales A manufacturer makes two models of an item: model I, which accounts for 80% of unit sales, and model II, which accounts for 20% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 10% of its model I and 18% of its model II. If a model is selected at random, find the probability that it will be defective Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the defect rate on m1 = .1
the defect rate on m2 = .18
m1 = model 1
m2 = model 2
t = total sales of m1 and m2
m1 = .8 * t
m2 = .2 * t
defective m1 = .1 * m1
defective m2 = .18 * m2
total defective = .1 * m1 + .18 * m2
since m1 = .8 * t and m2 = .2 * t, then:
total defective = .1 * .8 * t + .18 * .2 * t
simplify to get:
total defective = .116 * t = 11.6%
to see how this works, assume they sold a total of 1000 cars.
m1 was 80% of them = 800
m2 was 20% of them = 200
10% of m1 was defective = 10% of 800 = 80
18% of m2 was defective = 18% of 200 = 36
total defective = 116
percent defective of total = 116/1000 = .116 * 100 = 11.6%.
divide percent by 100 to get rate.
multiply rate by 100 to get percent.
