5. The probability that a defect will occur over the surface of a semiconductor chip is 0.2. Assuming the occurrences of defects are independent, what is the probability that two out of nine chips selected with replacement will be defective? 6. Assume that a component passes a test is 0.85 and that components perform independently. What is the probability that the third failure will occur on the tenth component tested? 7. Defects in poured metal caused by contamination follows a Poisson distribution with average number of occurrences being 2 per cubic millimeter. What is the probability that there will be at least three defects in a randomly selected cubic millimeter of this metal? R Problems: 8. Consider the distribution of problem 5. Make a table for the probability mass function. 9. Consider the distribution of problem 6. Graph this distribution. 10. Verify your solution for problem 7. Graph this distribution.
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For the first question, we need to find the probability that exactly two out of nine chips selected with replacement will be defective. We can use the binomial probability formula for this: $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$ where $n$ is the number of Show more…
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