Formulas and functions > Functions from A to Z > BINOMDIST (binomial distribution)

Note: BINOMDIST is supplemented by the new identical function BINOM.DIST and the completely new function BINOM.DIST.RANGE which are available in newer versions of Microsoft Excel (2010 or later).

Syntax:

BINOMDIST(k, n, p, Cumulative)

Description:

Returns the binomial distribution function.

The binomial distribution can be used to determine the probability to get k successes in an experiment with n independent trials with only two possible outcomes (success or failure) with a fixed probability of p for each trial.

For example, a coin flip experiment is a binomial experiment (see example below).

k is the number of successes. Must be in the range 0 to n.

n is the number of independent trial runs.

n and k should be integers. Digits right of the decimal point are ignored by PlanMaker.

p is the probability of a success for each trial run.

The logical value Cumulative lets you specify which type of function will be returned:

FALSE: The probability density function is returned. BINOMDIST thus determines the probability of having exactly k successes.

TRUE: The cumulative distribution function is returned. BINOMDIST thus determines the probability that there are at most k successes.

Example:

Let us take the above example:

When you flip a coin 10 times (n=10), what is the probability that it lands on "heads" (p=50%) exactly 4 times?

BINOMDIST(4, 10, 50%, FALSE) returns 0.20508 =20.5%

What is the probability that it lands on "heads" at most 4 times?

Here, instead of the density function, you use the distribution function (specify the Cumulative argument with TRUE):

BINOMDIST(4, 10, 50%, TRUE) returns 0.37695 =37.7%