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Select the best answer for each of the following questions Use the information below to answer questions (1-3) A batch of 500 containers for frozen orange juice contains 10 that are defective. Two are selected, at random, without replacement from the batch. 1. What is the probability that the second one selected is defective given that the first one was acceptable? A. 0.000361 B. 0.960361 C. 0.020040 D. 0.019639 E. None of the above 2. A. B. C. D. E. What is the probability that both are defective? 0.000361 0.960361 0.019639 0.981964 None of the above 3. A. B. C. D. E. What is the probability that both are acceptable? 0.999639 0.960361 0.019639 0.981964 None of the above Use the information below to answer questions (4-6) Customers are used to evaluate preliminary product designs. In the past 95% of highly successful products received good reviews, 60% of moderately successful products received good reviews, and 10% of poor products received good reviews. In addition, 40% of products have been highly successful, 35% have been moderately successful, and 25% have been poor products. 4. A. B. C. D. E. What is the probability that a product attains a good review? 0.385 0.615 0.057 0.035 None of the above 5. If a new design attains a good review, what is the probability that it will be a highly successful product? A. 0.987013 B. 0.382114 C. 0.051948 D. 0.617886 E. None of the above 6. If a product does not attain a good review, what is the probability that it will be a highly successful product? A. 0.987013 B. 0.617886 C. 0.051948 D. 0.948052 Use the information below to answer questions (7-8) The following circuit operates if and only if there a functional devices from left to right. Assume devices fail independently and that the probability of failure of each device is as shown. 0.1 0.1 0.2 7. A. B. C. D. E. What is the probability that the circuit operates? 0.55 0.9539 0.6156 0.9139 None of the above 8. A. B. C. D. E. What is the probability that all elements in the circuit operates? 0.55 0.9539 0.6156 0.9139 None of the above 0.05 Use the information below to answer questions (9-13) Given the following cumulative distribution function: 0 𝑥<1 𝐹(𝑥) = {0.5 1≤𝑥<3 1 3≤𝑥 9. 𝑃(1 < 𝑥 ≤ 2) = A. B. C. D. E. zero 0.5 0.75 1 None of the above 𝑃(𝑥 > 3) = 10. A. B. C. D. E. Zero 0.5 0.75 1 None of the above 𝑃(𝑥 = 3) = 11. A. B. C. D. E. Zero 0.5 0.75 1 None of the above 𝐸(𝑥) = 12. A. B. C. D. E. Zero 1 2 3 None of the above 𝑉(𝑥) = 13. A. B. C. D. E. Zero 0.5 0.75 1 None of the above Use the information below to answer questions (14-17) The life of a semiconductor laser at a constant power is normally distributed with a mean of 7000 hours and a standard deviation of 600 hours. 14. What is the probability that a laser fails before 5800 hours? A. 0.022750 B. 0.977250 C. 0.0455 D. 0.488625 E. None of the above 15. What is the life in hours that 90% of the lasers exceeds? A. 7500 B. 8200 C. 7774 D. 7600 16. What should the mean life equal in order for 99% of the lasers exceeds 10000 hours before failure? A. 11398 B. 5001 C. 8602 D. 5699 17. A product contains three lasers, and the product fails if any of the of the laser fails. Assume that the lasers fail independently. What should the mean life equal in order for 99% of the products exceed 10,000 hours before failure? A. 9899 B. 9500 C. 11632 D. 11398 18. The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. What is the probability of less than two views in 3 minutes? A. 0.061099 B. 0.011109 C. 0.049904 D. 0.112479 Use the information below to answer questions (19-20) A particularly long traffic light on your morning commute is green 20% of the time that you approach it. Assume that each morning represents an independent trial. 19. What is the probability that you need more than 4 days to find the light green on 3 mornings? A. 0.0336 B. 0.9664 C. 0.7696 D. 0.2304 E. None of the above 20. Over 13 mornings what is the probability that the light is green in more than 6 mornings? A. 0.03 B. 0.007 C. 0.0012 D. 0.9988 E. None of the above