Binomial inverse cumulative distribution function

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

`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].

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.

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