A Level Maths Notes: S2 – Normal Approximation to The Binomial Distribution and the Continuity Correction
The binomial 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 n is large - we must make
modifications since the binomial 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
and
The
normal approximation is
Look up the probability corresponding to
and
subtract from 1. This returns a probability of 0.0080.
may
be equal to 7, when we use the normal approximation
As
above
andThe
normal approximation is
Look up the probability corresponding to
and
subtract from 1 twice. This returns a probability of 0.9798.
may
be equal to 5, when we use the normal approximation
As
aboveandThe
normal approximation is
Look up the probability corresponding to
and
subtract from 1. This returns a probability of 0.0026
may
be equal to 5, when we use the normal approximation
As
aboveandThe
normal approximation is
Look up the probability corresponding to
and
subtract from 1 twice. This returns a probability of 0..9222.