An insurance company has a call center that makes cold calls

An insurance company has a call center that makes cold calls to individuals trying to sell life insurance.The probability of making a sale is 0.10. Assume binomial properties apply.If an individual in the center makes 20 calls, what is the probability they will make sales on more than 4 calls?

Solution

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.1      
x = our critical value of successes =    4      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   4   ) =    0.956825505
          
Thus, the probability of at least   5   successes is  
          
P(more than   4   ) =    0.043174495 [ANSWER]