Chapter 6 question 45 Please help A Tamiami shearing machine is producing 10% de

Question

Chapter 6 question 45 Please help A Tamiami shearing machine is producing 10% defective pieces,which is abnormally high. The quality control engineer has beenchecking the output by almost continuous sampling since theabnormal condition began. What is the probability that in a sampleof 10 pieces: a. Exactly 5 will be defective? b. 5 or more will be defective? Chapter 6 question 45 Please help A Tamiami shearing machine is producing 10% defective pieces,which is abnormally high. The quality control engineer has beenchecking the output by almost continuous sampling since theabnormal condition began. What is the probability that in a sampleof 10 pieces: a. Exactly 5 will be defective? b. 5 or more will be defective?

Explanation / Answer

Use binomial distribution with (n=10, p=.1). P(x) =C(n,x)p^x (1-p)^(n-x) where C(n,x)= n!/(x!(n-x)!). a. x=5 so P(5)=C(10,5)(.1)^5(.9)^5 = .0014883
b. P(5 or more defective) = 1- P(4 or less defective)                                          =  1- (P(0)-P(1)-P(2)-P(3)-P(4))                                         = 1- .9983651                                         = .0016

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