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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 7 examined that have a defective compressor. (a) Calculate P(X = 5) and P(X < 5). (Round your answers to four decimal places.) P(X = 5) = P(X s 5) = (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 500 refrigerators, of which 50 have defective compressors. If X is the number among 20 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X < 4) than to use the hypergeometric pmf. We can approximate the hypergeometric distribution with the --Select--- v distribution if the population size and the number of successes are large. Here n = and p = M/N = Approximate P(X < 4) using that method. (Round your answer to three decimal places.) P(X s 4) =

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 7 examined that have a defective compressor. (a) Calculate P(X = 5) and P(X < 5). (Round your answers to four decimal places.) P(X = 5) = P(X s 5) = (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 500 refrigerators, of which 50 have defective compressors. If X is the number among 20 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X < 4) than to use the hypergeometric pmf. We can approximate the hypergeometric distribution with the --Select--- v distribution if the population size and the number of successes are large. Here n = and p = M/N = Approximate P(X < 4) using that method. (Round your answer to three decimal places.) P(X s 4) =

Algebra & Trigonometry with Analytic Geometry
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 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 7 examined that have a defective compressor. (a) Calculate P(X = 5) and P(X < 5). (Round your answers to four decimal places.) P(X = 5) P(X < 5) = (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 500 refrigerators, of which 50 have defective compressors. If X is the number among 20 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X < 4) than to use the hypergeometric pmf. We can approximate the hypergeometric distribution with the ---Select-- v distribution if the population size and the number of successes are large. Here n = and p = M/N : Approximate P(X < 4) using that method. (Round your answer to three decimal places.) P(X < 4) -
Transcribed Image Text: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 7 examined that have a defective compressor. (a) Calculate P(X = 5) and P(X < 5). (Round your answers to four decimal places.) P(X = 5) P(X < 5) = (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 500 refrigerators, of which 50 have defective compressors. If X is the number among 20 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X < 4) than to use the hypergeometric pmf. We can approximate the hypergeometric distribution with the ---Select-- v distribution if the population size and the number of successes are large. Here n = and p = M/N : Approximate P(X < 4) using that method. (Round your answer to three decimal places.) P(X < 4) -
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