How this calculator works
An integer k represents the continuous strip from k - 0.5 to k + 0.5. Including k extends the relevant boundary outward by half a unit; excluding it moves the boundary inward. The returned normal probability uses the supplied count mean and SD. A continuity correction does not make an unsuitable normal approximation valid.
Formula
X=k → k-0.5<Y<k+0.5; X≤k → Y<k+0.5; X<k → Y<k-0.5; X≥k → Y>k-0.5; X>k → Y>k+0.5.
Worked example
For X ≤ 10, the corrected upper boundary is 10.5. A normal model with mean 10 and SD 1 then gives Φ(0.5) = 0.6914625.
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Frequently asked questions
Does the correction change the original count?
No. It changes the continuous approximation boundary.
Why half a unit?
Adjacent integer counts are one unit apart, so the halfway boundary is 0.5 away.
Can I use it for a proportion?
Translate the proportion event into an integer count first; the count step is one, while proportion steps are 1/n.