The Stat/List Editor’s binomial CDF is sometimes inaccurate.

[BlainUSM]

The function TIStat.binomCDF(n,p,low,up) may produce inaccurate answers when the parameter n is greater than a million.

I first noticed the error in the function during an in-class evaluation of the safety of commercial air flights, which happened to involve a binomial distribution with a large value of n. Here’s a similar example:

Input: TIStat.binomCDF(10^6,.00001,0,10)

Output: -3

The correct answer is approximately .58304, as indicated by Mathematica. For values of n less than a million, the function TIStat.binomCDF tends to agree with Mathematica. A binomial distribution may be defined that does not have the limitations of the one above:

Input: Define bi(n,p,l,u) = Σ(nCr(n,i)*p^i*(1-p)^(n-i),i,l,u)

Input: bi(10^6,.00001,0,10)

Output: .5830…

TI may have lessened the severity of this problem on newer 89’s; for all n ≥ 10^6, the function TIStat.binomCDF appears to return -3, an answer that is obviously not correct. On older TI-89’s, TIStat.binomCDF will sometimes return an inaccurate answer between 0 and 1, which could cause some confusion.