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Alex17521 [72]
3 years ago
9

"is it appropriate to use the normal approximation for the sampling distribution of"

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
5 0

Answer: Normal approximation can be used for discrete sampling distributions, such as Binomial distribution and Poisson distribution if certain conditions are met.

Step-by-step explanation: We will give conditions under which the Binomial and Poisson distribitions, which are discrete, can be approximated by the Normal distribution. This procedure is called normal approximation.

1. Binomial distribution: Let the sampling distribution be the binomial distribution B(n,p), where n is the number of trials and p is the probability of success. It can be approximated by the Normal distribution with the mean of np and the variance of np(1-p), denoted by N(np,np(1-p)) if the following condition is met:

n>9\left(\frac{1-p}{p}\right)\text{ and } n>9\left(\frac{p}{1-p}\right)

2. Poisson distribution: Let the sampling distribution be the Poisson distribution P(\lambda) where \lambda is its mean. It can be approximated by the Normal distribution with the mean \lambda and the variance \lambda, denoted by N(\lambda,\lambda) when \lambda is large enough, say \lambda>1000 (however, different sources may give different lower value for \lambda but the greater it is, the better the approximation).

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