ach of 13 refrigerators of a certain type has been retu to a use of an audible, hig mese refrigerators have a defective compressor and the other 5 have less serious problems. If the refi examined that have a defective compressor. (a) Calculate P(X= 5) and P(X ≤ 5). (Round your answers to four decimal places.) P(X = 5) = P(X ≤ 5) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (RC TE S

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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 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 7
examined that have a defective compressor.
(a) Calculate P(X= 5) and P(X ≤ 5). (Round your answers to four decimal places.)
P(X = 5) =
P(X ≤ 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 15 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
and p = M/N =
n=
--Select---
Approximate P(X ≤ 3) using that method. (Round your answer to three decimal places.)
P(X ≤ 3) *
this question.
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 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 7 examined that have a defective compressor. (a) Calculate P(X= 5) and P(X ≤ 5). (Round your answers to four decimal places.) P(X = 5) = P(X ≤ 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 15 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 and p = M/N = n= --Select--- Approximate P(X ≤ 3) using that method. (Round your answer to three decimal places.) P(X ≤ 3) * this question.
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