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sci.binomial-distribution Calculator
Calculates binomial probability P(X=k) = C(n,k)p^k(1−p)^(n−k) and cumulative CDF for n trials with success probability p. Normal approximation is valid when np > 5 and n(1−p) > 5 — for rare events (p < 0.01), Poisson with λ=np is a better approximation.
Inputs
N Trials
Count of items or occurrences.
P Success
Reference formula or conversion factor shown for context.
K Successes
Count of items or occurrences.
Results
P(X=k) probability
Reference formula or conversion factor shown for context.
C(n,k) combinations
The value at the specified point or condition.
mean μ = np
Arithmetic average — sum divided by count. Simple and familiar, but pulled by outliers. If your data contains extreme values, the median may be more representative.
std dev σ = √(np(1-p))
Standard deviation -- the average spread of values around the mean. In a normal distribution: 68% within 1 SD, 95% within 2 SD.