Question 129435: Suppose that it is known that 5% of the items produced by a particular machine are defective in some way, and that we will choose a random sample of exactly 20 parts made by this machine.
a.What is the expected number of defective items, out of the 20 we select?
b.What is the probability that exactly 1 of the 20 items is defective?
c. what is the probability that no more than 2 out of the 20 items selected are defective.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose that it is known that 5% of the items produced by a particular machine are defective in some way, and that we will choose a random sample of exactly 20 parts made by this machine.
a.What is the expected number of defective items, out of the 20 we select?
0.05*20 = 1
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b.What is the probability that exactly 1 of the 20 items is defective?
P(x=1) = 20C1(0.05)(0.95)^19 = 0.377...
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c. what is the probability that no more than 2 out of the 20 items selected are defective.
P(0<=x<=2) = binomcdf(20,0.05,2)= 0.9245...
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Comment: The binomcdf is a function on a TI calculator.
For example binomcdf(20,0,05,2) = 20C0(0.05)^0+0.95^20 + 20C1(0.05)(0.95)^19
+ 20C2(0.05)^2(0.95)^18 = 0.9245...
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Cheers,
Stan H.
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