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

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.

RELATED QUESTIONS
A manufacturer makes two models of an item:modelI,which accounts for 80% of unit... (answered by robertb)

Model one accounts for 80% of unit sales and model two for 20% of unit sales. However,... (answered by edjones)

A Manufacturer of microcomputers produces three different models as shown in Table 2. The (answered by Theo)

Please I have put this question up several times and no one has given me an answer. A... (answered by ankor@dixie-net.com)

Thanks for your help--- A company makes two models of a product. The times (in hours)... (answered by narayaba,stanbon)

admission to the circus costs $8 for adults and $6 for children. a total of 900 tickets... (answered by Simnepi)

For each problem, use meaningful variables to write a linear function to model the... (answered by Theo)

A & B Pty Ltd manufactures window air-conditioners in both a deluxe model and a... (answered by CPhill)

Hi Tutor, I need help for this question. I tried, but not sure the answer. "A... (answered by scott8148)