WORKSHEET
                      From Poisson & Normal Approximations to Binomial Distribution
Objective:
To identify the conditions under which the Binomial distribution, B(n, p) can be approximated 
using Poisson distribution Po(np) or Normal Distribution N(np, np(1-p)).
Procedure:
1) Input a set of values for n, p and X into the simulation.
2) Record the probabilities of the Binomial, Normal and Poisson Distributions in table 1.1.
3) Vary the values for n, p and X.
4) Repeat step 1,2 and 3 for tables 1.2, 2.1 and 2.2
5)  Compare the probabilities and write down your observations.
6) Deduce the appropriate approximation (Poisson or Normal) for the Binomial Distribution.
and record your answer in the summary table.
Tabulations:
Part I: When  n is small (say n =10)
Table 1.1:  p     0.1 such that np
n p np nq
 
Binomial Probability Normal Probability Poisson Probability
From To
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
Table 1.2:  p     0.1 such that np       5
n p np nq
 
Binomial Probability Normal Probability Poisson Probability
From To
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
Observation(s):
When n is small and np         , the Binomial probability can be approximated by using a
_______________probability.
When n is small and np > 5, the Binomial probability can be approximated by using a
_______________probability.
Part II: When  n is large (say n =100)
Table 2.1:  p     0.1 such that np
n p np nq
 
Binomial Probability Normal Probability Poisson Probability
From To
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
Table 2.2:  p     0.1 such that np       5 and nq        5
n p np nq
 
Binomial Probability Normal Probability Poisson Probability
From To
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
    0 0          
Observation(s):
When n is large and np         , the Binomial probability can be approximated by using a
_______________probability.
When n is large and np > 5, the Binomial probability can be approximated by using a
________________probability.
Summary:
Fill in the appropriate approximation for the given conditions.