Answer:
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 <em>more</em> than 19 org. is equal to <em>one substracting the probability of having equal or less</em> 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.