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The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"t proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with u = 1. (Round your answers to three decimal places.) (a) Obtain P(X s 4) by using the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X S 4) = (b) Determine P(X = 1) from the pmf formula. P(X = 1) = Determine P(X = 1) from the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X = 1) = | (c) Determine P(1 sXS 3). P(1 sXS 3) = (d) What is the probability that X exceeds its mean value by more than one standard deviation? You may need to use the appropriate table in the Appendix of Tables to answer this question.

The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"t proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with u = 1. (Round your answers to three decimal places.) (a) Obtain P(X s 4) by using the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X S 4) = (b) Determine P(X = 1) from the pmf formula. P(X = 1) = Determine P(X = 1) from the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X = 1) = | (c) Determine P(1 sXS 3). P(1 sXS 3) = (d) What is the probability that X exceeds its mean value by more than one standard deviation? You may need to use the appropriate table in the Appendix of Tables to answer this question.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need part b) and d) thank you

The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"t proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with u = 1. (Round your answers to three decimal places.) (a) Obtain P(X < 4) by using the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X < 4) = (b) Determine P(X = 1) from the pmf formula. P(X = 1) = Determine P(X = 1) from the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X = 1) = (c) Determine P(1 < X < 3). P(1 < X< 3) = (d) What is the probability that X exceeds its mean value by more than one standard deviation? You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:The article "Expectation Analysis of the Probability of Failure for Water Supply Pipes"t proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with u = 1. (Round your answers to three decimal places.) (a) Obtain P(X < 4) by using the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X < 4) = (b) Determine P(X = 1) from the pmf formula. P(X = 1) = Determine P(X = 1) from the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X = 1) = (c) Determine P(1 < X < 3). P(1 < X< 3) = (d) What is the probability that X exceeds its mean value by more than one standard deviation? You may need to use the appropriate table in the Appendix of Tables to answer this question.
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