Continuity Correction Calculator
Apply a continuity correction when approximating a discrete binomial probability with the continuous normal distribution. Enter your value of x, the comparison, and the binomial parameters to get the corrected boundary and z-score.
What This Calculator Does
When approximating a discrete binomial distribution with the continuous normal distribution, a continuity correction adjusts the boundary by 0.5 to account for the fact that the binomial only takes whole-number values while the normal curve is continuous.
How the Correction Works
Depending on which probability you want, the boundary shifts by ±0.5:
- P(X ≤ x) becomes P(Y < x + 0.5)
- P(X < x) becomes P(Y < x − 0.5)
- P(X ≥ x) becomes P(Y > x − 0.5)
- P(X > x) becomes P(Y > x + 0.5)
- P(X = x) becomes P(x − 0.5 < Y < x + 0.5)
The corrected boundary is then converted to a z-score using z = (boundary − np) / √(np(1−p)), which can be looked up in a standard normal table to get the approximate probability. This correction meaningfully improves accuracy when n is only moderately large. For general statistics education and coursework use.