A binomial distribution may be approximated by a poisson distribution whena.n is small and p is smallb.n is large and p is largec.n is large and p is smalld.n is small and p is large
Question
A binomial distribution may be approximated by a poisson distribution whena.n is small and p is smallb.n is large and p is largec.n is large and p is smalld.n is small and p is large
Solution
The binomial distribution may be approximated by a Poisson distribution when n is large and p is small. So, the correct answer is c. n is large and p is small.
Here's why:
The Poisson distribution is an approximation to the binomial distribution for a fixed mean with large n (number of trials) and small p (probability of success on each trial). This approximation is useful because the mathematics underpinning the Poisson distribution is simpler than that underpinning the binomial distribution.
In other words, if you have a large number of trials (n is large) and the probability of success in any given trial is small (p is small), then the binomial distribution of these trials is approximately a Poisson distribution.
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