Which of the following binomial distributions can be well approximated by a normal distribution? A Poisson distribution? Both? Neither? (d)n=1000,p=.001

Tobias Ali 2020-12-03 Answered
Which of the following binomial distributions can be well approximated by a normal distribution? A Poisson distribution? Both? Neither?
(d)n=1000,p=.001
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Expert Answer

unett
Answered 2020-12-04 Author has 119 answers

The Rule of five:
The normal with means np and np q can be used to approximate the binomial distribution with parameters n and p if npq>5.
Here, n=1,000,p=0.001.
npq=1,000×0.001×0.999=0.999<5
Normal approximation cannot be used for the binomial distribution with n=1,000,p=0.001.
The direct approximation of the binomial by Poisson says that the binomial distribution with parameters n and p has the same distribution as the Poisson with the parameter np when npis large.
The value of np is obtained as shown below:
np=1,000×0.001=1
Since the value of n is large and p is small and the value of np is small, the binomial distribution can be approximated to Poisson.
That is, the binomial distribution with n=1,000, p=0.001 cannot be approximated to a normal distribution and it can be approximated to a Poisson distribution.

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