The number of "successes" in *n* independent
trials that each have the same probability *p* of success
has the binomial
distribution with parameters *n* and *p*.

For example, the number of heads in 10 tosses of a fair coin
has a binomial distribution with parameters *n*=10 and *p*=50%.

The expected
value of the binomial distribution is *n×p* (that's
where the probability histogram would balance), and the standard
error of the binomial distribution is
(*n*×*p*×(1-*p*))^{½}.

Note that for a fixed value of *n*, the distribution is
broadest (has the largest SE) when *p* = 50%.

You can use the scrollbars to select different parts of the histogram; the area of the selected region is printed in the middle.

The normal approximation to the binomial probability histogram
is good when *n* is large and *p* is neither close
to 0 nor close to 100%.

The "Show Normal Curve" button superposes the normal approximation to the binomial over the binomial histogram.

The "Area from" and "to" scrollbars and text boxes allow you to select a range of possible "successes," for which the applet will calculate the probability, displayed after "Selected area."

The text boxes on the bottom row let you change
the number of trials *n* and the probability *p* of
success in each trial. To change the value, delete the value in
the box, type in the new value, then strike the "enter"
or "return" key or click the mouse anywhere outside the
box.