Suppose the probability that a randomly selected PGA Tour pl

Suppose the probability that a randomly selected PGA Tour player uses a Titleist brand golf ball is 0.85. For a smple of 8 PGA Tour players, find the probability that no less than 7 use a Titleist brand golf ball.

Solution

Note that P(at least 7) = 1 - P(at most 6).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    8      
p = the probability of a success =    0.85      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   6   ) =    0.342816969
          
Thus, the probability of at least   7   successes is  
          
P(at least   7   ) =    0.657183031