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obability that X exceeds its mean value by more than 1 standa shipment of 400 refrigerators, of which 40 have defective comp at least approximately) P(X s 3) than to use the hypergeomet ate the hypergeometric distribution with the Select-

obability that X exceeds its mean value by more than 1 standa shipment of 400 refrigerators, of which 40 have defective comp at least approximately) P(X s 3) than to use the hypergeomet ate the hypergeometric distribution with the Select-

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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ASK YOUR TEACHER 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 8 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 s 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 20 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 n- We can approximate the hypergeometric distribution with the Select- P = M/N- 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. PRACTICE ANOTHER and
Transcribed Image Text:ASK YOUR TEACHER 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 8 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 s 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 20 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 n- We can approximate the hypergeometric distribution with the Select- P = M/N- 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. PRACTICE ANOTHER and
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