Question

if a baseball players batting average is .320 find the probability that the player will get at most 26 hits in 100 times at bat

Answer 1

Here we are dealing with binominal distribution. You can find additional info here:
https://en.wikipedia.org/wiki/Binomial_distribution

What we are asked to find is cumulative distribution function for k=26, n=100, p=0.32

So we just use formula
F(x,n,p) = I_{1-p} (n-k,k+1) = I_{0.68} (74,27)

where I_x (a,b) is regularized beta function. You can read about it by following this link:
https://en.wikipedia.org/wiki/Regularized_incomplete_beta_function#Incomplete_beta_function

Using, for example, Wolfram Mathematica we find that
I_{0.68} (74,27) = 0.118016 and that's our answer