Binomial Process Variance Calculator
Calculate variance, standard deviation, and confidence intervals for binomial distributions with ease
Binomial Parameters
Advanced Options
Binomial Distribution Results
Enter parameters to calculate confidence intervals.
Detailed Analysis
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📊 Binomial Distribution Visualization
📚 Binomial Distribution Properties
Definition
The binomial distribution describes the number of successes in a fixed number of independent trials, each with the same probability of success.
Parameters
n = number of trials
p = probability of success
q = 1-p = probability of failure
Formulas
μ = n×p
σ² = n×p×(1-p)
σ = √(n×p×(1-p))
Applications
Quality control, medicine, finance, survey analysis, and any yes/no outcome scenario with fixed trials.
📝 Normal Approximation Guidelines
| Approximation | Rule of Thumb | When to Use |
|---|---|---|
| Normal Approximation | n×p ≥ 10 and n×(1-p) ≥ 10 | For calculating probabilities when n is large |
| Poisson Approximation | n ≥ 20 and p ≤ 0.05 | For rare events with large n |
| Exact Binomial | Any n and p | When approximations don't meet criteria |
Note: These are guidelines - always check your specific situation's requirements.
Note: This calculator provides statistical estimates based on binomial distribution theory. For critical applications, consult with a qualified statistician.