Problem 4. Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m^3 [the article \"Counting at Low Concentrations: The Statistical Challenges of Verifying Ballast Water Discharge Standards\" (Ecological Applications, 2013: 339-351)]. What is the probability that one cubic meter of discharge contains at least 8 organisms? [Hint: Use the cumulative distribution table] What is the probability that the number of organisms in 1.5 m^3 of discharge exceeds its mean value by more than one standard deviation? [Hint: Use the cumulative distribution table] Solution Possion Distribution PMF of P.D is = f ( k ) = e- x / x! Where = parameter of the distribution. x = is the number of independent trials Mean = Organisms are with a concentration of 10 Organisms/meter^3 a) CONTAIN ATLEAST 8 ORGANISMS P( X < 8) = P(X=7) + P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) = e^-10 * 0 ^ 7 / 7! + e^-10 * ^ 6 / 6! + e^-10 * ^ 5 / 5! + e^-10 * ^ 4 / 4! + e^-10 * ^ 3 / 3! + e^- 10 * ^ 2 / 2! + e^-10 * ^ 1 / 1! + e^-10 * ^ 0 / 0! = 0.2202 P( X > = 8 ) = 1 - P (X < 8) = 0.7798.