6.1.5—Normal distribution

A binomial or Poisson count may be approximated by N(μ,σ²) when its distribution is sufficiently spread. Convert integer events to intervals using continuity correction, such as P(X≤k)≈P(Y<k+0.5).

State μ and σ² from the original model, standardise the corrected boundary and compare the approximation with an exact calculation when accuracy matters.

P(X≤10) becomes P(Y<10.5), not P(Y≤10), under a continuous normal approximation.

The normal variable is continuous, so forgetting the half-unit correction can materially shift a tail probability.