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 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.) P(X= 7) = 0.5035 ✔ P(X ≤ 7): 0.5035 x (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) 0.0139 x (c) Consider a large shipment of 700 refrigerators, of which 70 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 ≤ 5) than to use the hypergeometric pmf. ✔✔✔ distribution if the population size and the number of successes are large. Here n = 25 We can approximate the hypergeometric distribution with the binomial P=M/N=0.1 Approximate P(X ≤ 5) using that method. (Round your answer to three decimal places.) P(X ≤ 5) = in the Appendix of Tables to answer this question. ✔and
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 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.) P(X= 7) = 0.5035 ✔ P(X ≤ 7): 0.5035 x (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) 0.0139 x (c) Consider a large shipment of 700 refrigerators, of which 70 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 ≤ 5) than to use the hypergeometric pmf. ✔✔✔ distribution if the population size and the number of successes are large. Here n = 25 We can approximate the hypergeometric distribution with the binomial P=M/N=0.1 Approximate P(X ≤ 5) using that method. (Round your answer to three decimal places.) P(X ≤ 5) = in the Appendix of Tables to answer this question. ✔and
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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