Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m (the article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standardst considers using the Poisson process for this purpose). (a) What is the probability that one cubic meter of discharge contains at least 7 organisms? (Round your answer to three decimal places.) (b) What is the probability that the number of organisms in 1.5 m of discharge exceeds its mean value by more than two standard deviations? (Round your answer to three decimal places.) (c) For what amount of discharge would the probability of containing at least 1 organism be 0.9957 (Round your answer to two decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.
Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m (the article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standardst considers using the Poisson process for this purpose). (a) What is the probability that one cubic meter of discharge contains at least 7 organisms? (Round your answer to three decimal places.) (b) What is the probability that the number of organisms in 1.5 m of discharge exceeds its mean value by more than two standard deviations? (Round your answer to three decimal places.) (c) For what amount of discharge would the probability of containing at least 1 organism be 0.9957 (Round your answer to two decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.
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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Transcribed Image Text:Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m (the article "Counting
at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standardst considers using the Poisson process for this purpose).
(a) What is the probability that one cubic meter of discharge contains at least 7 organisms? (Round your answer to three decimal places.)
(b) What is the probability that the number of organisms in 1.5 m of discharge exceeds its mean value by more than two standard deviations? (Round
your answer to three decimal places.)
(c) For what amount of discharge would the probability of containing at least 1 organism be 0.995? (Round your answer to two decimal places.)
m
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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