slaggingV

2021-01-02

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

yagombyeR

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, $n=300$, $p=0.05$.
$npq=300×0.05×0.95=14.25\ge 5$
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.

Do you have a similar question?