The JO Supplies Company buys calculators from a Korean suppl

The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 14 calculators are selected at random, what is the probability that less than 5 of the calculators will be defective?

Solution

Note that P(fewer than x) = P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    14      
p = the probability of a success =    0.1      
x = our critical value of successes =    5      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   4   ) =    0.990769788
          
Which is also          
          
P(fewer than   5   ) =    0.990769788 [ANSWER]