SOLUTION: A machine that manufactures automobile parts is estimated to produce defective parts 6% of the time. If this estimate is correct, and 8 parts produced by this machine are randomly

Algebra ->  Probability-and-statistics -> SOLUTION: A machine that manufactures automobile parts is estimated to produce defective parts 6% of the time. If this estimate is correct, and 8 parts produced by this machine are randomly       Log On


   

Question 364644: A machine that manufactures automobile parts is estimated to produce defective parts 6% of the time. If this estimate is correct, and 8 parts produced by this machine are randomly selected, what is the probability that at least 2 turn out to be defective? Round your answer to four decimal places.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

Note: The probability of x successes in n trials is: 

.

P = nCx* p%5Ex*q%5E%28n-x%29 where p and q are the probabilities of success and failure respectively. 

In this case p = .06 and q = .94 

nCx = n%21%2F%28x%21%28n-x%21%29%29



P(at least 2 turn out to be defective)

1 - P(0 def) - P(1 defect)

P(0 def) = .94^8 = .610

P(1 defect) = 8C1*.06^1 .94^7 = 8*.06^1 .94^7 = 8*.06*.648 = .311

1 - .921 = .079