Assumptions of the Poisson Distribution
(1)
The probability is proportional to the length of the
interval.
(2)
The intervals are independent.
Also known as the "Law of Improbable Events"
Limited form of Binomial (very small
S
, very large n)
203

Poisson Probability Distribution
The Poisson probability distribution is characterized by
the number of times an event happens during some
interval or continuum.
Examples include:
• The number of misspelled words per page in a
newspaper.
• The number of calls per hour received by Dyson
Vacuum Cleaner Company.
• The number of vehicles sold per day at Hyatt Buick
GMC in Durham, North Carolina.
• The number of goals scored in a college soccer game.
203
Poisson Probability Distribution
The
Poisson
distribution can be
described mathematically using the
formula:
204

Poisson Probability Distribution
z
The mean number of successes
ȝ
can be
determined in binomial situations by
n
S
, where
n
is the number of trials and
S
is the probability of a
success.
z
The variance of the Poisson distribution is also
equal to
n
S
.
204
Assume baggage is rarely lost by Northwest Airlines. Suppose
a random sample of 1,000 flights shows a total of 300 bags
were lost. Thus, the arithmetic mean number of lost bags
per flight is 0.3 (300/1,000). If the number of lost bags per
flight follows a Poisson distribution with
μ
= 0.3, find the
probability of not losing any bags in a specific flight.
What is the Interval?
A FLIGHT
NOTE:
μ
calculated by observation, NOT
n
S
Poisson Probability Distribution -
Example
204

Poisson Probability Distribution - Table
Recall from the previous illustration that the number of lost bags
follows a Poisson distribution with a mean of 0.3. Use Appendix B.5
to find the probability that no bags will be lost on a particular flight.
What is the probability
exactly one bag
will be lost on a particular
flight?
205
Example from text - variation
(comparing Poisson vs. Binomial):
we'll just do P(0), not 1 - P(0)
z
Probability of hurricane hitting in a year is 0.05
z
What is the probability of 0 in 30 years?
z
Poisson:
z
Binomial:
206
S
P
n
#
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)
(
x
e
x
P
u
x
0
P
x
n
x
x
n
C
x
P
0
0
)
1
(
)
(
S
S
22313
.
0
!
0
5
.
1
)
0
(
5
.
1
5
.
1
0
0
0
e
e
P
5
.
1
05
.
0
30
x
#
P
21464
.
0
95
.
0
)
05
.
1
(
30
30
0
n
P
)
1
(
)
0
(
S
0

More About the Poisson Probability
Distribution
•The Poisson probability distribution is always positively skewed and
the random variable has no specific upper limit.
•The Poisson distribution for the lost bags illustration, where
μ=0.3, is
highly skewed. As μ becomes larger, the Poisson distribution becomes
more symmetrical.
207
MGMT 2340
Section
W01
Business Statistics I
Instructor:
E. Mark Leany
contact via
Blackboard
online.uen.org
alternately:
[email protected]

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- Spring '11
- Leany
- Poisson Distribution, Probability distribution, Probability theory, Binomial distribution, Discrete probability distribution