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