The POISSON Probability Function is a discrete probability distribution function used to calculate the number of successes "

[ *To calculate the probability of random variables which are distributed
POISSON we will follow a very similar procedure to the one just described*.]

**Sample Problem**

Let's say we want to find the probability of **4 **flaws
in a **10** yard piece of material where it is known that
this material has an average of only **1**
flaw every ** 5 **yards.** **Here
our** given**

We first need to calculate our expected value, ,
for **10** yards. We will use the information
given:

(**1**flaw / **5**yards)
* **10** yards = **2** flaws. This is our __ __.We
would use the formula: **P(x) = [(** **^x)(e^(-(**
**)]
/ x ! **with **=2**
and **x=4.**

On the calculator we go to the distribution menu by pressing **
**
Next **Arrow up** to "**B : poissonpdf ( ".
(left screen will be displayed) **

Press (you will see the right screen)

Now we must enter **,
x **in that order so for our problem we enter **.
**Press
**
.0902235222 **will be displayed. This is the probability of

** "Poissoncdf ("** will give the cumulative probability from
0 through X. **(**e.g. **poissoncdf (2,4)** will give the probability of **x = 0+1+2+3+4
, **where =2**)**

You should get 0.9473469827 for the cumulative answer.

To see a **Distribution Plot** of a particular **POISSON**
distribution we will need to enter some data into the **LIST. **

*Recall the discussion from the Binomial Distribution Plot. (see mini-lesson
4) *

We will enter the "**x**" values {**1,2,3,4,5,6,7,8,9,10**}
into **L1** and the **POISSON Formula **into **L2 . **

Press
**"EDIT" **should be highlighted. Press **
**

Enter the numbers {**1,2,3,4,5,6,7,8,9,10}** into **List1**. These are
the **"x"** values. Next we want to enter the **formula** into
**List2**.

First highlight ** L2 (**you should see lower left screen**)**

Next enter

**LN **.

(You should see this text scroll across the screen)

We now need to finish the formula by dividing by ** L1 **factorial.

So press (see lower left screen)

**Arrow left** to "**PRB"** and
press
(see upper screen)

Now press **
List2 **will be filled with these probabilities

(see screen below)

The numbers in **List2** are the probabilities associated with the **"x"**
values in **List1**.

To see a plot go to the **STAT PLOT **so press **
**

(see screen below)

**"1:Plot1"** should be highlighted.

Press
(see screen)

Make sure **On** is highlighted and press

Next **Arrow down** and highlight the **plot**
option. Press

Make sure **Xlist: L1 , Ylist: L2**

Now, as always, we need to adjust the **window** to fit our data, or you
may press **
**

To adjust the window press Match these settings:

** Xmin: 0 , Xmax: 11 ,Xscl 1 , Ymin: 0 ,Ymax: 0.8 , Yscl 0.1** .

Press then ( you will see this screen)

*(Notice this graph more closely resembles a negative exponential curve*
*rather than a “bell curve”.* )

Here "**x**" is the number of
successes and "**y**" is the corresponding probability. So from this screen we
see that there is a **.27067057** probability
of **2** flaws from **10**
yards of material where there is an average of only **1**
flaw every **5** yards. You can **Arrow left** or **right** to
read each desired probability.

*Notice also that in the upper left screen P1: L1,L2*