Continuity Correction Calculator - Normal Approximation to Binomial
Calculate continuity-corrected z-scores and probabilities when approximating discrete distributions with normal distribution
Binomial Parameters
Results
Correction Explanation
What is a Continuity Correction Calculator?
A Continuity Correction Calculator applies the adjustment needed when approximating discrete probability distributions with the continuous normal distribution, improving approximation accuracy.
This calculator is used for:
- Normal Approximation - Approximate binomial with normal distribution
- Probability Calculation - More accurate discrete probability estimates
- Hypothesis Testing - Improved test statistic calculations
- Statistical Analysis - Better approximations for large samples
To calculate exact binomial probabilities before applying corrections, explore our Binomial Distribution Calculator to determine probabilities for discrete binary outcomes.
To understand normal distribution percentages, check out our Empirical Rule Calculator to see how data falls within standard deviations of the mean.
To learn about sampling distributions underlying normal approximations, visit our Central Limit Theorem Calculator to understand how distributions approach normality.
To work with confidence intervals for your estimates, use our Confidence Interval Calculator to determine ranges for population parameters.
How Continuity Correction Works
Correction rules for different probability types:
Then calculate z-score: z = (corrected value - μ) / σ
Key Concepts Explained
Discrete vs Continuous
Discrete distributions have distinct values; continuous distributions span ranges. The correction bridges this gap.
The 0.5 Adjustment
Adding or subtracting 0.5 converts point values to intervals, matching how continuous distributions represent discrete values.
Validity Conditions
Normal approximation is valid when np ≥ 5 and n(1-p) ≥ 5. Otherwise, use exact binomial probabilities.
How to Use This Calculator
Enter Binomial Parameters
Input number of trials (n) and success probability (p)
Enter X Value
Specify the value for probability calculation
Select Probability Type
Choose the type of probability you need
Benefits of This Calculator
- Automatic Correction - Applies correct adjustment for each type
- Validity Check - Verifies if normal approximation is appropriate
- Clear Explanation - Shows why correction is applied
- Educational Tool - Learn continuity correction principles
- Improved Accuracy - Better than uncorrected approximation
- Multiple Types - Handles all probability inequality types
Factors Affecting Results
- Sample Size - Larger n improves normal approximation accuracy
- Probability p - Values near 0.5 give better approximations
- np and n(1-p) - Both should be ≥ 5 for validity
- Extreme Values - Tails of distribution need more care
- Probability Type - Different types require different corrections
- Precision Needs - Very precise work may need exact binomial
Frequently Asked Questions
What is continuity correction?
Continuity correction is an adjustment made when approximating a discrete distribution (like binomial) with a continuous distribution (like normal). It adds or subtracts 0.5 to improve accuracy of the approximation.
When should you use continuity correction?
Use continuity correction when approximating discrete probability distributions with the normal distribution, particularly for binomial distributions when np ≥ 5 and n(1-p) ≥ 5.
How do you apply continuity correction?
For P(X = k), use P(k - 0.5 < X < k + 0.5). For P(X ≤ k), use P(X < k + 0.5). For P(X ≥ k), use P(X > k - 0.5). For P(X < k), use P(X < k - 0.5).
Why is continuity correction important?
Continuity correction improves the accuracy of normal approximation to discrete distributions by accounting for the fact that discrete values represent intervals on the continuous scale.
What is the continuity correction formula?
The correction adjusts discrete values by ±0.5: for P(X ≤ k) use k + 0.5, for P(X ≥ k) use k - 0.5, and for P(X = k) use the interval [k - 0.5, k + 0.5].
When can you skip continuity correction?
With very large sample sizes (n > 100), the impact of continuity correction becomes minimal. However, it's still recommended for better accuracy, especially near the distribution tails.