Merlot Assignment-Project Synergy

 

Using the Poisson Distribution as an Approximation for the Binomial Distribution

by Angela Walters – Capitol College

 

Course: Any class dealing with elementary statistics.

 

Uses the Merlot website “VassarStats:Website for Statistical Computation” by Richard Lowry

 

Background: The Poisson distribution may be used to approximate the Binomial distribution under certain conditions. The rule of thumb used to verify that the Poisson distribution may be used to approximate the Binomial distribution is that n – the number of items in the sample be 100, and n times p(the probability of a success in a binomial experiment)  10. The Poisson distribution is given by the following formula:

 

                        ,  where

 

 

Assignment:

 

1. Given a binomial distribution with n = 550 and p = 0.02. Use the Poisson distribution to to compute the probability of getting k = 20 and k = 35 successes.

 

2. Go to the site http://faculty.vassar.edu/lowry/VassarStats.html  and select Distributions. Scroll down the Distributions page until you see the Poisson distribution link. Select the link. Scroll to the bottom of the Poisson distribution page and select continue. When prompted for n enter 552 and for p enter 0.02.

 

 

3. Find the value for k = 20 successes.

 

 

4. Find the value for k = 35 successes.

 

 

 

5. How does the result from the Poisson distribution agree with a binomial distribution having x = 20 and x = 35?