Poisson Distribution Calculator
The Poisson Calculator makes it easy to compute individual and cumulative
Poisson probabilities. For help in using the calculator, read the
FrequentlyAsked Questions or review the
Sample Problems.
To learn more about the Poisson distribution, read Stat Trek's
tutorial on the Poisson distribution.
 Enter a value in BOTH of the first two text boxes.
 Click the Calculate
button.
 The Calculator will compute the Poisson and
Cumulative Probabilities.




FrequentlyAsked Questions
Instructions: To find the answer to a frequentlyasked
question, simply click on the question. If none of the questions addresses your
need, refer to Stat Trek's tutorial
on the Poisson distribution or visit the
Statistics Glossary. Online help is just a mouse click away.
Poisson Distribution: Sample Problems

Historically, schools in a Dekalb County close 3 days each year, due to snow.
What is the probability that schools in Dekalb County will close for 4 days
next year?
Solution:
We know the following:

The Poisson random variable is 4.

The average rate of success is 3. Here, we define a "success" as a school
closing. Since the schools have closed historically 3 days each year due to
snow, the average rate of success is 3.
Therefore, we plug those numbers into the Poisson
Calculator
and hit the Calculate button. The calculator reports that the Poisson
probability is 0.168. That is the probability of getting EXACTLY 4 school
closings due to snow, next winter. (The calculator also reports the cumulative
probability  the probability of getting AT MOST 4 school closings in the
coming year. The cumulative probability is 0.815.)

An expert typist makes, on average, 2 typing errors every 5 pages. What is the
probability that the typist will make at most 5 errors on the next fifteen
pages?
Solution:
We know the following:

The Poisson random variable is 5.

The average rate of success 6. This may require a little explanation. We know
that the average rate of success is 2 errors for every five pages. However,
this problem calls for typing three times as many pages, so we would expect the
typist to make three times as many errors, on average. Therefore, average rate
of success is 3 x 2, which equals 6.
Therefore, we plug those numbers into the Poisson
Calculator and hit the Calculate button. The calculator reports that
the P(X < is 0.446. In other words, the probability
that the typist makes no more than 5 errors is 0.446. (Note that the calculator
also displays the Poisson probability  the probability that the typist makes
EXACTLY 5 errors. The Poisson probability is 0.161.)