Organisms are present in ballast water discharged from a shi

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\" (Ecological Applications, 2013: 339-351)]. a. What is the probability that one cubic meter of discharge contains at least 8 organisms? [Hint: Use the cumulative distribution table on Moodle] b. What is the probability that the number of organisms in 1.5 m3 of discharge exceeds its mean value by more than one standard deviation? [Hint: Use the cumulative distribution table on Moodle]

Solution

a) From poisson tables P[X>= 8] = 1 -P[X<8] = 1 - 0.2202 = 0.7798