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.