As with the binomial distribution there is a table that we can
use under certain conditions that will make calculating probabilities
a little easier when using the Poisson Distribution.
Our author provides tables that list the probabilities for the
following values of 
: 0.1, 0.2, 0.3,
.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 2, 3, 4, 5, 6, 7, 8, and 9. One
catch, our author uses the symbol 
for
the mean of a Poisson Distribution. I use 
because many texts use it to distinguish this mean from the means
of other distributions such as the normal distribution
(stay tuned).
Of the 2 problems that we've discussed, the only one we can use
the table for is the "waitress" problem. The "football
injury" problem has 
= 3.2, a value
that does not show up in the table.
Ex. On an average Friday, a waitress gets no tip from 5 customers.
Find the probability that she will get no tip from 7 customers
this Friday.
The waitress averages 5 customers that leave no tip on Fridays
: 
= 5.
Random Variable : The number of customers that leave her no tip this Friday.
We are interested in 
.
Here's the table.
To use the table, go across until you find the value of 
that goes with your problem. Then go down that column until you
reach the row(s) that contain the number of successes that you
are interested in. Then read the table.
From above we see that the probability that there will be 7 customers
that leave no tip this Friday is 0.1044. Which method was easier?
Suppose we were interested in the probability that at least
7 customers left no tip. Then which method is easier? Clearly
the table.
