SOLUTION: It is estimated that 1.3% of all items produced on an assembly line have some form of defect. You randomly selected 60 items for inspection. What is the probability that more than

Question 1187215: It is estimated that 1.3% of all items produced on an assembly line have some form of defect. You randomly selected 60 items for inspection.
What is the probability that more than 1.5% of the 60 items have some form of defect?
The probability is 86% that the proportion of items with a defect is less than what numbers?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
What is the probability that 1 or more have some form of defect, since 0.015*60=0.9 items and an integer has to be used?
That is 1- probability that none has a defect or 1-0.987^60=0.5439
the probability that 0 have a defect is 0.987^60=0.4561
probability that 1 item has a defect is 60C1*0.013*0.987^59=0.3604
probability that 2 items have a defect is 60C2*0.013^2*0.987^58=0.1400
probability that 3 items have a defect is 60C3*0.013^3*0.987^57=0.0357
The answer is fewer than 3 items. Fewer than 2 items has a probability of 81.65% and fewer than 3 has a probability of 95.65%.

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