Question 959078: Two percent of the parts produced by a machine are defective. Twenty parts are selected at random. Use the binomial probability tables to answer the following questions.
a. What is the probability that exactly 3 parts will be defective?
b. What is the probability that the number of defective parts will be more than 2 but fewer than 6?
c. What is the probability that fewer than 4 parts will be defective?
d. What is the expected number of defective parts?
e. What is the variance for the number of defective parts?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Two percent of the parts produced by a machine are defective. Twenty parts are selected at random. Use the binomial probability tables to answer the following questions.
Binomial Problem with n = 30 and p(defective) = 0.02
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a. What is the probability that exactly 3 parts will be defective?
P(x = 3) = 20C3*0.02^3*0.98^17 = binompdf(20,0.02,3) = 0.0065
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b. What is the probability that the number of defective parts will be more than 2 but fewer than 6?
P(3<= x <=5) = binomcdf(20,0.02,5)-binomcdf(20,0.02,2) = 0.0071
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c. What is the probability that fewer than 4 parts will be defective?
P(0<= x <=3) = binomcdf(20,0.02,3) =
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d. What is the expected number of defective parts?
Ans:: mean = np = 20*0.02 = 2/5 = 0.4
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e. What is the variance for the number of defective parts?
variance = npq = 0.4*0.98 = 0.392
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Cheers,
Stan H.
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