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Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m3 (the article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standards"t 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 m3 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 0.991? (Round your answer to two decimal places.) m3

Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m3 (the article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standards"t 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 m3 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 0.991? (Round your answer to two decimal places.) m3

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Title: Understanding Poisson Processes in Ballast Water Discharge** **Introduction:** Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m³. The article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standards" considers using the Poisson process for this purpose. **Exercises:** **(a)** What is the probability that one cubic meter of discharge contains at least 7 organisms? (Round your answer to three decimal places.) *Answer Box: __________* **(b)** What is the probability that the number of organisms in 1.5 m³ of discharge exceeds its mean value by more than two standard deviations? (Round your answer to three decimal places.) *Answer Box: __________* **(c)** For what amount of discharge would the probability of containing at least 1 organism be 0.991? (Round your answer to two decimal places.) *Answer Box: __________ m³* **Discussion:** These exercises explore the application of the Poisson distribution to model the presence of organisms in ballast water discharge, crucial for environmental standards and regulations. Understanding this process helps in making informed decisions about ecological safety in maritime operations.
Transcribed Image Text:**Title: Understanding Poisson Processes in Ballast Water Discharge** **Introduction:** Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m³. The article "Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standards" considers using the Poisson process for this purpose. **Exercises:** **(a)** What is the probability that one cubic meter of discharge contains at least 7 organisms? (Round your answer to three decimal places.) *Answer Box: __________* **(b)** What is the probability that the number of organisms in 1.5 m³ of discharge exceeds its mean value by more than two standard deviations? (Round your answer to three decimal places.) *Answer Box: __________* **(c)** For what amount of discharge would the probability of containing at least 1 organism be 0.991? (Round your answer to two decimal places.) *Answer Box: __________ m³* **Discussion:** These exercises explore the application of the Poisson distribution to model the presence of organisms in ballast water discharge, crucial for environmental standards and regulations. Understanding this process helps in making informed decisions about ecological safety in maritime operations.
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