Mastering Mathematics Smartly
by Wee Wen Shih
A unique self-help website that provides comprehensive coverage of mathematics at A-level & beyond, written in a student-friendly style.
Poisson approximation to Binomial
To use the Poisson approximation, check that:
(1) n is large, i.e. greater than 50;
(2) np is small, i.e. less than 5.
The resulting Poisson distribution has mean = np.
No continuity correction is required.
Try this!
When normal approximations fail
Suppose we are solving a question involving B(n, p) and we have: n is large, np > 5 but nq < 5. Remember that q = 1 - p.
We have unwittingly gone into a situation where the normal approximation cannot be applied at all.
The strategy: change B(n, p) to B(n, q).
When we do this, we will have: n is large and nq < 5. In this case we can use, without any worry, the Poisson approximation i.e. Po(nq).
