Which of the following binomial distributions can be well approximated by a normal distribution? A Poisson distribution? Both? Neither? (b)n=300,p=.05

slaggingV 2021-01-02 Answered
Which of the following binomial distributions can be well approximated by a normal distribution? A Poisson distribution? Both? Neither?
(b)n=300,p=.05
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Expert Answer

yagombyeR
Answered 2021-01-03 Author has 92 answers
The Rule of five:
The normal with mean np and npq can be used to approximate the binomial distribution with parameters n and p if npq>5.
Here, n=300, p=0.05.
npq=300×0.05×0.95=14.255
Normal approximation can be used for the binomial distribution with n=300, p=0.05.
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 parameter np when np is large.
The value of np is obtained as shown below:
np=300×0.05=15
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=300, p=0.05 can be approximated to a normal distribution and to a Poisson distribution.
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