Each of 11 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppos that 8 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 numbe 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) 1.6363 x 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 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. ✔ distribution if the population size and the number of successes are large. Here We can approximate the hypergeometric distribution with the binomial n = 10 ✓and p = M/N=0.1 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.
Each of 11 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppos that 8 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 numbe 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) 1.6363 x 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 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. ✔ distribution if the population size and the number of successes are large. Here We can approximate the hypergeometric distribution with the binomial n = 10 ✓and p = M/N=0.1 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.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 6E: Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the...
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Transcribed Image Text:Each of 11 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppos
that 8 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 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)
1.6363
X
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 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.
distribution if the population size and the number of successes are large. Here
We can approximate the hypergeometric distribution with the binomial
n = 10
and p = M/N=0.1
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.
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