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A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 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 10 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X S 2)
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(Xx S 2) using that method. (Round your answer to three decimal places.)
P(X $2)
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 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 10 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X S 2) 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(Xx S 2) using that method. (Round your answer to three decimal places.) P(X $2)
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