# Thread: Problem using poisson Approximation

1. ## Problem using poisson Approximation

If the probability that an individual suffers from bad reaction from an injection of a given serum is 0.001, determine the probability that out of 2000 individuals

i) exactly 3 individuals will suffer a bad reaction
ii) more than 2 individuals will suffer a bad reaction
by using Poisson Approximation

Also give exact probability (you need not simplify the expression)

2. Originally Posted by Stats
If the probability that an individual suffers from bad reaction from an injection of a given serum is 0.001, determine the probability that out of 2000 individuals

i) exactly 3 individuals will suffer a bad reaction
ii) more than 2 individuals will suffer a bad reaction
by using Poisson Approximation

Also give exact probability (you need not simplify the expression)
Poisson approximation: The mean is $\lambda = (0.001)(2000) = 2$. Substitute this into the pmf of the Poisson distribution and use the pmf to do the calculations.

What do you think the exact distribution is?

For (ii) note that $\Pr(X > 2) = 1 - \Pr(X \leq 2)$.

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### if the probability that an individual suffers a bad reaction from injection

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