A recent survey found that 65 of all adults over 50 wear gla

A recent survey found that 65% of all adults over 50 wear glasses for driving. In a random sample 10 adults over 50, what is the probability that at least six wear glasses?

Solution

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.65      
x = our critical value of successes =    6      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   5   ) =    0.248504491
          
Thus, the probability of at least   6   successes is  
          
P(at least   6   ) =    0.751495509 [ANSWER]