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(a) Calculate P(X= 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X= 4) = 2 X P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X ≤ 2) than to use the hypergeometric pmf. ✓distribution if the population size and the number of successes are large. Here We can approximate the hypergeometric distribution with the ---Select--- and p = M/N = n = Approximate P(X ≤ 2) using that method. (Round your answer to three decimal places.) P(X ≤ 2) =

(a) Calculate P(X= 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X= 4) = 2 X P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X ≤ 2) than to use the hypergeometric pmf. ✓distribution if the population size and the number of successes are large. Here We can approximate the hypergeometric distribution with the ---Select--- and p = M/N = n = Approximate P(X ≤ 2) using that method. (Round your answer to three decimal places.) P(X ≤ 2) =

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 8 of these refrigerators have a defective compressor and the other 4 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (a) Calculate P(X= 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X= 4) = 2 x P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X ≤ 2) than to use the hypergeometric pmf. h ✓distribution if the population size and the number of successes are large. Here We can approximate the hypergeometric distribution with the ---Select--- and p = M/N = n = Approximate P(X ≤ 2) using that method. (Round your answer to three decimal places.) P(X ≤ 2) = You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 8 of these refrigerators have a defective compressor and the other 4 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (a) Calculate P(X= 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X= 4) = 2 x P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X ≤ 2) than to use the hypergeometric pmf. h ✓distribution if the population size and the number of successes are large. Here We can approximate the hypergeometric distribution with the ---Select--- and p = M/N = n = Approximate P(X ≤ 2) using that method. (Round your answer to three decimal places.) P(X ≤ 2) = You may need to use the appropriate table in the Appendix of Tables to answer this question.
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