Assume that a procedure yields a binomial distribution with

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.

n=21, x=3, p=0.15

P(3) = ? (Round to three decimal places as needed)

Solution

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    21      
p = the probability of a success =    0.15      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.240805322 [answer]