A particular type of tennis racket comes in a midsize versio

A particular type of tennis racket comes in a midsize version and an oversize version. Sixty percent of all customers at a certain store want the oversize version. (Round your answers to three decimal places.) (a) Among ten randomly selected customers who want this type of racket, what is the probability that at least six want the oversize version?

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 =    0.6      
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   ) =    0.366896742
          
Thus, the probability of at least   6   successes is  
          
P(at least   6   ) =    0.633103258 [answer]