Each of 11 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppos that 8 of these refrigerators have a defective compressor and the other 3 have less serious problems. If the refrigerators are examined in random order, let X be the numbe among the first 6 examined that have a defective compressor. (a) Calculate P(X= 4) and P(X s 4). (Round your answers to four decimal places.) P(X=4) 1.6363 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 10 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X ≤ 3) 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 binomial n = 10 ✓and p = M/N=0.1 Approximate P(X ≤ 3) using that method. (Round your answer to three decimal places.) P(X ≤ 3) = You may need to use the appropriate table in the Appendix of Tables to answer this question.

Each of 11 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppos that 8 of these refrigerators have a defective compressor and the other 3 have less serious problems. If the refrigerators are examined in random order, let X be the numbe among the first 6 examined that have a defective compressor. (a) Calculate P(X= 4) and P(X s 4). (Round your answers to four decimal places.) P(X=4) 1.6363 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 10 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X ≤ 3) 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 binomial n = 10 ✓and p = M/N=0.1 Approximate P(X ≤ 3) using that method. (Round your answer to three decimal places.) P(X ≤ 3) = You may need to use the appropriate table in the Appendix of Tables to answer this question.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Each of 14 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 9 of these refrigerators have a defective compressor and the other 5 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. (I have figured out part "a" but need help with "b" and P(X ≤ 3) in "c") (a) Calculate P(X = 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X = 4) = 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)…
Each of 14 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 9 of these refrigerators have a defective compressor and the other 5 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)= ? 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 ≤ 3) than to use the hypergeometric pmf. We can approximate the…
2. Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of a high-pitched oscillating noise when the refrigerator is running. Suppose that four of these 12 have defective compressors and the other eight have less serious problems. If they are examined in random order, let ? be the number among the first six examined that have a defective compressor. Compute (a) ?(? = 1), (b) ?(? ≥ 4), and (c) ?(1 ≤ ? ≤ 3).
Each of 13 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 10 of these refrigerators have a defective compressor and the other 3 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 9 examined that have a defective compressor. (a) Calculate P(X = 7) and P(X ≤ 7). (Round your answers to four decimal places.) (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.)
Each of 13 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 10 of these refrigerators have a defective compressor and the other 3 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 9 examined that have a defective compressor. ***Please solve both parts or do not attempt this problem.*** (a) Calculate P(X ≤ 7). (Round your answer to four decimal places.) (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.)
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