The Poisson distribution, written
has Expectation Value
This is the expected number of successes in n attempts. The variance is given by
If we want to use the normal distribution as an approximation to estimate
for example – which is very useful when
and
are large - we must make modifications since the Poisson distribution is a discrete distribution but the normal approximation is continuous.
In order to take account of this, and that if we are estimating
may be equal to 5, when we use the normal approximation
Suppose
The normal approximation is
Look up the probability corresponding to
and subtract it from 1. This returns a probability of 0.0778..
may be equal to 7, when we use the normal approximation
As above
The normal approximation is
Look up the probability corresponding to
and subtract from 1 twice. This returns a probability of 0.6335
may not be equal to 5, when we use the normal approximation
As abovethe normal approximation is
Look up the probability corresponding to
and subtract it from 1. This returns a probability of 0.0409.
may not be equal to 7, when we use the normal approximation
As aboveThe normal approximation is
Look up the probability corresponding to
and subtract it from one twice. This returns a probability of 0.7148.