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 ) what is the probability that one cubic meter of discharge contains at least 8 organisms? (round your answer to three decimal ) 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? (round your answer to three decimal ) for what amount of discharge would the probability of containing at least 1 organism be 0.994? (round your answer to two decimal places.) m3

a) The probaility is 0.333.

b) The probability is 0.125.

c) The volume is 0.512 m3.

Step-by-step explanation:

Organisms are present in ballast water discharged with a concentration of 10 organisms/m3.

That is our rate of the Poisson process

a) The probability of having at least 8 organisms is equal to the sum of the probabilities of having from 0 to 8 organisms:

Note: In this case, the volume V is 1 m3.

b) In this case, the volume is 1.5m3 so we have to multiply the rate by 1.5. Then it becomes:

The standard deviation of this distribution is

We have to calculate the probability of exceeding 19 organisms in 1.5m3:

We have that the probability of having more than 19 org. is equal to one substracting the probability of having equal or less than 19 org:

c) We have to calculate the volume such that there is a probability P=0.994 of having at least one organism in the water. This can be calculated as one less the probability of having zero organisms.

the answer is d

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