For a binomial distribution with p = 0.20 and n = 100, what is the probability of obtaining a score less than or equal to x = 12? hint: use interval-based calculations because no critical region is involved.

The binomial distribution is given by, 
P(X=x) =  
q = probability of failure = 1-0.2 = 0.8
n = 100
They have asked to find the probability of obtaining a score less than or equal to 12.
∴ P(X≤12) = 
                    where, x = 0,1,2,3,4,5,6,7,8,9,10,11,12                  
∴ P(X≤12) =  +  +  +  +  +  + 

Evaluating each term and adding them you will get,
P(X≤12) = 0.02532833572
This is the required probability.