View source for Statistics for Decision Makers - 05.06 - Probability - Poisson Distribution

{{Cat|Statistics for Decision Makers|05.05}}
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;title: 05.06 - Probability - Poisson Distribution
;author: Bernard Szlachta (NobleProg Ltd) bs@nobleprog.co.uk
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== Poisson Distribution。 ==
Calculating randomly scattered events in time or in space.

[[File:ClipCapIt-140604-155006.PNG]]


; Examples
* The number of road accidents in given period.
* The goals scored in a soccer match.
* The number of Losses/Claims occurring in a given period.
* The number of customers calling in a day.

== Formula。 ==
In order to apply the Poisson distribution, the various events must be independent. 


The general formula of the Poisson distribution is:
 [[File:ClipCapIt-140526-182302.PNG]]
 e is the base of natural logarithms (2.7183)
 μ is the mean number of "successes"
 x is the number of "successes" in question

==Example。==
* The mean number of customer calls to your company on a weekday is 8.
* What is the probability that on a given weekday there would be 11 calls? 

:[[File:ClipCapIt-140604-151220.PNG|380px]]


;Solution
 [[File:ClipCapIt-140526-182254.PNG|100px]]
 
 In a spreadsheet
 '''=POISSON(11,8,false)'''
The probability of having 11 calls is 0.072.

=Quiz。=
[[Statistics_for_Decision_Makers_-_05.06_-_Probability_-_Poisson_Distribution#Quiz|Please find the Quiz here]]

=Quiz= 
<quiz display=simple>

{The mean number of defective products produced in a factory in one day is 21. What is the probability that in a given day there are exactly 12 defective products?

|type="{}"}
{ 0.012 | .012 }

{
{{Show Answer|
0.012

0.012 can be obtained using the formula.
}}
}


{Which of these can be computed using the Poisson distribution?
|type="[]"}
-The average waiting time between phone calls.
+The number of people killed accidentally by horse kicks.

{Which of these can be computed using Poisson distribution?
|type="[]"}
+The number of enquiries via online form in a month.
-The probability of selecting a person over 2 metres high.