A survey of US adults ages 25 and older found that 86 have a

A survey of U.S adults ages 25 and older found that 86% have a high school diploma. You randomly select 30 U.S. adults ages 25 and older. Find the probability that the number who have a high school diploma is exactly 25.

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 =    30      
p = the probability of a success =    0.86      
x = the number of successes =    25      
          
Thus, the probability is          
          
P (    25   ) =    0.176577193 [answer]