Let's say you want to compute the probability
where
converges in distribution to
, and
follows a normal distribution. The normal approximation (without the continuity correction) basically involves choosing
such that its mean and variance are the same as those for
.
Example: If
is binomially distributed with
and
, then
has mean
and variance
. So you can approximate a probability in terms of
with a probability in terms of
:
where
follows the standard normal distribution.