the following question i have done, but my answer is incorrect.
A company receives 70% of its orders over the internet. On a particular day it receives 32 independent orders. Calculate the probability that between 20 and 30 (both inclusive) of the orders are received over the internet?
This is what i have done
Pr(20 <= X <= 30) = Pr(X <=30) - Pr(X <= 20) = binomcdf(32,.7,30)-binomcdf(32,.7,20) = .7715
However when i done binomcdf(32,.7,30)-binomcdf(32,.7,19) = 0.864 which is the correct answer, but don't understand how this is correct.
according to the question if "both inclusive" shouldn't it be Pr(20 <= X <= 30) ?