6.5.2—Normal approximation

Approximate a binomial count by N(np,np(1−p)) or a Poisson count by N(λ,λ) when the distribution is sufficiently spread. Apply continuity correction to integer boundaries.

Translate “at most”, “at least” and exact counts into half-unit intervals before standardising, then compare with the exact model when the approximation is marginal.

P(X≥12) becomes P(Y>11.5) in the continuous approximation.

Using the uncorrected boundary can produce a visibly different tail probability.