A Level Maths Notes: S2 – Normal Approximation to The Poisson Distribution and the Continuity Correction
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.