$n=$		$p=$
$x=$		P(X = x)  = P(X ≤ x)  = P(X ≥ x)  =

Inference method: Wald Score Agresti-Coull Clopper-Pearson Blaker

80% 90% 95% 99% CI for $p$:

$H_0:p$ = ≥ ≤
$H_a:p$ ≠ > <

This applet computes probabilities for the binomial distribution: $$X \sim Bin(n, p)$$

Directions

• Enter the number of trials in the $n$ box.
• Enter the probability of success in the $p$ box.
• Hitting "Tab" or "Enter" on your keyboard will plot the probability mass function (pmf).

To compute a probability, select $P(X=x)$ from the drop-down box, enter a numeric $x$ value, and press "Enter" on your keyboard. The probability $P(X=x)$ will appear in the pink box. Select $P(X \leq x)$ from the drop-down box for a left-tail probability (this is the cdf).

Details

• $f(x)=P(X=x)={n \choose x}p^x(1-p)^{n-x}$
  for $x=0,1,\ldots,n$
• $\mu=E(X)=np$
• $\sigma^2=Var(X)=np(1-p)$
• $\sigma=SD(X)=\sqrt{np(1-p)}$