Cumulative binomial probability tables give are used to find #P(X<=x) #for the distribution #X~B(n,p)#
Using some basic rules you can work out many different probabilities of a binomial distribution:
#P(X < x) = P(X <= x-1)#
#P(X >= x)= 1-P(X <= x-1)#
#P(X > x)= 1-P(X <= x)#
#P(A < X <= B) = P(X <=B) - P(X <= A)#
... and so on.
There is a seperate table for each sample size ("#n#") so first find the correct table of #n#=your sample size.
Then find the column on that table with the probability "#p#" of your distribution. The the number in the row #x=a# is #P(X <=a )#
ie. to find #P(4 <= X <= 9)# for the the distribution #X~B(14, 0.55)#, go to the table for #n=14#. Then find the column #p=0.55#. Look for the row #x=9# in that column, which gives 0.8328, and then look for #x=3# in that column, which gives 0.0114.
So #P(4 <= X <= 9) = 0.8328-0.0114=0.8214#
