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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 defective compressor. (a) Calculate P(X = 4) and P(X s 4). (Round your answers to four decimal places.) P(X = 4) - 4196 P(X S 4) = .5944 (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) .0699 (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 s 3) than to use the hypergeometric pmf. We can approximate the hypergeometric distribution with the binomial v distribution if the population size and the number of successes are large. Here n = 10 v and p = M/N - 40/400 Approximate P(X S 3) using that method. (Round your answer to three decimal places.) P(X s 3) * 7636

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 defective compressor. (a) Calculate P(X = 4) and P(X s 4). (Round your answers to four decimal places.) P(X = 4) - 4196 P(X S 4) = .5944 (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) .0699 (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 s 3) than to use the hypergeometric pmf. We can approximate the hypergeometric distribution with the binomial v distribution if the population size and the number of successes are large. Here n = 10 v and p = M/N - 40/400 Approximate P(X S 3) using that method. (Round your answer to three decimal places.) P(X s 3) * 7636

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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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. (a) Calculate P(X 4) and P(X < 4). (Round your answers to four decimal places.) P(X = 4) .4196 P(X < 4) 5944 (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) .0699 (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. We can approximate the hypergeometric distribution with the binomial distribution if the population size and the number of successes are large. Here n = 10 and p M/N 40/400 Approximate P(X < 3) using that method. (Round your answer to three decimal places.) P(X < 3) - .7636
Transcribed Image Text: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) .4196 P(X < 4) 5944 (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) .0699 (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. We can approximate the hypergeometric distribution with the binomial distribution if the population size and the number of successes are large. Here n = 10 and p M/N 40/400 Approximate P(X < 3) using that method. (Round your answer to three decimal places.) P(X < 3) - .7636
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