# binoinv

Binomial inverse cumulative distribution function

## Syntax

```X = binoinv(Y,N,P) ```

## Description

`X = binoinv(Y,N,P)` returns the smallest integer `X` such that the binomial cdf evaluated at `X` is equal to or exceeds `Y`. You can think of `Y` as the probability of observing `X` successes in `N` independent trials where `P` is the probability of success in each trial. Each `X` is a positive integer less than or equal to `N`.

`Y`, `N`, and `P` can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs. The parameters in `N` must be positive integers, and the values in both `P` and `Y` must lie on the interval [0 1].

## Examples

If a baseball team has a 50-50 chance of winning any game, what is a reasonable range of games this team might win over a season of 162 games?

```binoinv([0.05 0.95],162,0.5) ans = 71 91```

This result means that in 90% of baseball seasons, a .500 team should win between 71 and 91 games.

## Version History

Introduced before R2006a