The article \"Expectation Analysis of the Probability of Failure for Water Suppl

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 o ailures s 1 very dose to one of the cases considered in the article Then x, the number of ai res, has a Posson distribution with 1 Round your answers to three decimal places.) (a) Obtain PX S 5) by using the Cumulative Poisson Probabilities table in the Appendix of Tables. (b) Determine P(X-2) from the pmf formula Determine PX2) from the Cumulative Poisson Probabilities table in the Appendix of Tables. P(X-2) (c) Determine P(2 4). (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

Explanation / Answer

a) Use Excel function

POISSON.DIST(5,1,TRUE) = 0.999

b) Use Excel function

POISSON.DIST(2,1,FALSE) = 0.184 (same by both method)

C) Use Excel function

POISSON.DIST(4,1,TRUE) -POISSON.DIST(2,1,TRUE)

= 0.077

d) Here Standard deviation is also same as mean = 1

P(X>2)

Use excel function

1-POISSON.DIST(5,1,TRUE)

= 0.080

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