Business Statistics I Dr. Changping Wang
6.3. Poisson Distribution
• A discrete probability distribution.
• Satisfies the following conditions:
(1) The experiment consists of counting the number of times an event,
x, occurs in a given interval. The interval can be an interval of time, area,
(2) The probability of the event occurring is the same for each interval.
(3) The number of occurrences in one interval is independent of the
number of occurrences in other intervals.
• The probability of exactly x occurrences in an interval is
P(X =x)= e μx
where is the mean number of occurrences, and e ≈ 2.71828 ...
Note: The variance of X is also equal to . μ
The Poisson random variable (probability distribution) was introduced by
S.D. Poisson (French, 17811840) in 1837. The Poisson random
variable has a tremendous range of applications in diverse area because
it may be used as an approximation for a binomial distribution with
parameters (n, p) when n is large and p is small enough so that μ = np is a
Some examples of random variables that usually obey
the Poisson probability law.
1) The number of misprints on a page (or a group of pages) of a book.
2) The number of people in a community living to 100 years of age.
Session 8 Page 1 Business Statistics I Dr. Changping Wang
3) The number of wrong telephone numbers that are dialed in a day.
4) The number of packages of dog food sold in a particular store each
5) The number of customers entering in a post office on a given day.
6) The number of passengers waiting for a street car during a time
period on a bus stop.
7) The number of earthquakes in an area during a year.
8) The number of suicides in a city in a given month.
9) The number of accidents per month at a certain intersection.
Session 8 Page 2 Business Statistics I Dr. Changping Wang
Example 2: Customers arrive randomly at a local bank at an average
rate of 3 every 3 minutes. Find the probability that
a) none of customers arrive in a 3minute period?
b) more than 10 customers arrive in a 12minute period?
Session 8 Page 3 Business Statistics I Dr. Changping Wang
c) at least 15 customers arrive in a 24minute period?
Calculator Lesson 3 (Page 290): How to use Calculator to
compute the Poisson probabilities?
Step 1: Use STAT mode
Step 2: Use the F6 key to get the following menu
RPH ] CALC ] TEST ] [INTR ] DIST ] [>> ]
F1 F2 F