· To the binomial distribution
· To the Poisson distribution
If your A level maths syllabus refers to the Normal approximation, then this blog post is for you! In many circumstances, both of these discrete distributions look very much like the Normal distribution.
This video clip gives an overview of approximating with the Normal distribution.
Using the Normal distribution to approximate either/both of these has effectively become redundant, due to advances in technology, because anyone with access to the internet or a calculator with distribution menus - can compute probabilities directly and exactly for any binomial or Poisson distribution.
But if you do need to approximate, then you simply calculate mean and standard deviation for your distribution and then use these values for the approx Normal model:
Continuity Corrections
When calculating probabilities, we adjust values of X with a continuity correction because we have moved from a discrete random variable to a continuous random variable. Applying the cc will make your answer a little more accurate. This is explained more dynamically in the video clip above.
As you can see, the approximate values for cumulative probabilities are very close to the exact values. There are some rules of thumb to check whether the approximation will be good. Typically these are large n for the binomial, with p close to 0.5. For the Poisson, typically we want the mean to be 20 or more.
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