### Binomial Distribution$X \sim Bin(n, p)$

 $n=$ $p=$ $x=$ P(X = x)  = P(X ≤ x)  = Normal Approximation

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).

If $n \geq 30$, $np \geq 5$, and $n(1-p) \geq 5$, then the normal approximation checkbox can be selected. This approximates the binomial probability (with continuity correction) and graphs the normal pdf over the binomial pmf.