Continuity Correction Calculator

When approximating a discrete distribution like the binomial distribution using a continuous normal distribution, rectangles representing discrete values must be adjusted to match continuous intervals. This involves adding or subtracting 0.5 from the discrete target value (n2). First, the mean and standard deviation are calculated using the formulas μ = n × p and σ = √(n × p × (1 - p)). Next, the adjusted value is integrated into the Z-score formula: z = (n2 ± 0.5 - μ) / σ. Finally, standard normal distribution tables or cumulative distribution functions convert the Z-score into accurate probability percentages.

Imagine a scenario where a fair coin is flipped 100 times (n = 100) with a success probability of p = 0.5 for landing heads. We want to find the probability of getting exactly or at most 60 heads. First, compute the mean: μ = 100 × 0.5 = 50. Next, compute the variance and standard deviation: σ² = 100 × 0.5 × 0.5 = 25, so σ = 5. To find the probability for at most 60 successes using continuity correction, we adjust 60 upward by 0.5 to 60.5. Calculating the Z-score gives z = (60.5 - 50) / 5 = 10.5 / 5 = 2.11. Looking up this Z-score yields a cumulative probability of approximately 0.9826, representing our corrected normal approximation.

Always verify that your sample size satisfies the conditions for a normal approximation, typically requiring both n × p ≥ 5 and n × (1 - p) ≥ 5. Remember to subtract 0.5 for 'at least' or 'greater than' scenarios and add 0.5 for 'at most' or 'less than' scenarios to maintain directional accuracy. Double-check whether your specific problem requires a strict inequality adjustment or an inclusive boundary condition.