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The Poisson distribution as an approximation of the Binomial.

The Poisson distribution as an approximation of the Binomial. When the number of trials in a Binomial distribution is very large, and the probability of success is very small, then np ~ npq (as q ~ 1), therefore it is possible to change the distribution to a Poisson distribution.

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The Poisson distribution as an approximation of the Binomial.

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  1. The Poisson distribution as an approximation of the Binomial. When the number of trials in a Binomial distribution is very large, and the probability of success is very small, then np ~ npq (as q ~ 1), therefore it is possible to change the distribution to a Poisson distribution. We will only have an approximation of the probability. In order to change from Binomial to the Poisson, we need to calculate the mean. X ~ B ( 500 , 0.01 ) Mean = np = 500 x 0.01 = 5 The approximation is therefore Y ~ Po ( 5 )

  2. Example X is the number of defective screws in a packet of 1000 screws. X has a Binomial distribution X ~ B ( 1000 , 0.003 ) Calculate the probability that 2 or more of the screws are defective. Since X ~ B ( 1000 , 0.003 ), Y ~ Po(1000 x 0.003) Y ~ Po(3) P(X ≥ 2)  P(Y ≥ 2) = 0.8009

  3. Exercise 4.7 Mathematics Statistics Unit S1 - WJEC Homework 8 Homework 9

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