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2021-01-02

Which of the following binomial distributions can be well approximated by a normal distribution? A Poisson distribution? Both? Neither?

(b)$n=300$ ,$p=.05$

(b)

yagombyeR

Skilled2021-01-03Added 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,$n=300$ , $p=0.05$ .

$npq=300\times 0.05\times 0.95=14.25\ge 5$

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:

$np=300\times 0.05=15$

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.

The normal with mean np and npq can be used to approximate the binomial distribution with parameters n and p if

Here,

Normal approximation can be used for the binomial distribution with

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:

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

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