At a particular spot in a local lake, there are, on average, 25 fish per cubic meter.If we assume that the probability of finding a fish is the same in this region over all cubic meters of water and that the number of fish in any one cubic meter in this region is independent of the number in any other cubic meter, what is the probability that we will find exactly 12 fish in the cubic meter in which we are fishing?
A) 0.0017
B) 0.0004
C) 0.4800
D) 0.0480

Question

Quizplus · Accepted Answer

The probability of finding exactly 12 fish in a cubic meter is given by the Poisson distribution:P(X = k) = (e^-λ * λ^k) / k!where λ is the average number of fish per cubic meter.In this case, λ = 25, so the probability of finding exactly 12 fish is:P(X = 12) = (e^-25 * 25^12) / 12! = 0.0017

At a Particular Spot in a Local Lake, There Are