Question

A major flooding in a given year has a Poisson distribution with a mean occurrence of 2.5

d) How many months have to pass to be in the 80th percentile?

Thank you!!

Answer 1

We have to use the Poisson distribution table to find the answer.

Let x be the number of months has major flooding incidents .

We are given = 2.5 and asked to find x such that sum of probabilities up to that x is 0.8

So first we need probabilities for each x with = 2.5

So first we need to find cumulative probabilities for each x ..So we goes on adding the each probability to its previous probability

The cumulative for x = 0 would be P(X) = 0.0821

The cumulative for x = 1 would be 0.0821 + 0.2052 = 0.2873

The cumulative for x = 2 would be 0.2873 + 0.2565 = 0.5438

Similarly we have to find cumulative for all x

Since the cumulative for x = 4 is 0.8912 , so it exceeds 0.8 at x = 4 first time

The required number of months would be 3

Because the percentile or sum of probabilities up to x = 3 is approximately equal to 0.80

Therefore approximately 3 months have to pass to be in the 80th percentile