Mathematics: 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?

only one line can be drawnStep-by-step explanation:...

Organisms are present in ballast water discharged

Ответ:

helper49

05.01.2022

Mathematics

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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ 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 $\mu = 10$

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

This is $P(X \geq 6)$ . 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