Binomial Distribution Calculator

Your details

How many independent trials are run. Must be a whole number (0-1000).
trials
The chance of success on a single trial, between 0 and 1.
Exact gives P(X = k) plus all cumulative variants. Interval gives P(r0 <= X <= r1) and its complement.
The exact number of successes to target (0 to n).
successes
P(X = k)
0.205078

Probability of exactly k successes.

P(X <= k)0.376953
P(X >= k)0.828125
P(X < k)0.171875
P(X > k)0.623047
Mean (mu)5
Variance (sigma^2)2.5
Std deviation (sigma)1.5811
Skewness0
Excess kurtosis-0.2

The chance of exactly 4 successes in 10 trials is 20.508%.

  • On average you would expect 5 successes across 10 trials (mean = np).
  • There is a 37.7% chance of 4 or fewer, and a 82.81% chance of 4 or more.
  • The distribution is skewed symmetric (p near 0.5); skewness = 0.
  • Excess kurtosis is -0.2: the tails are flatter than a normal curve (platykurtic).

Next stepSwitch to Interval mode to find the probability of a range like P(3 <= X <= 7), or adjust p to model a biased coin.

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