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). what is the probability that one cubic meter of discharge contains at least 6 organisms?

There is a 93.28% probability that one cubic meter of discharge contains at least 6 organisms.

Step-by-step explanation:

The number of organisms in a cubic meter of discharge is a Poisson process. So, we use the following definition:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

is the Euler number

is the mean in the given time interval.

Organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms/m3. This means that

What is the probability that one cubic meter of discharge contains at least 6 organisms?

This is . We know that either we have less than 6 organisms, or we have at least 6 organism. The sum of the probabilities is decimal 1. So

In which

.

Each one of these probabilities can be found by the poisson formula.

So

So

Finally

There is a 93.28% probability that one cubic meter of discharge contains at least 6 organisms.

the reporter's right

step-by-step explanation:

1/4 = .25 / 25%