Suppose that 55 of all babies born in a particular hospital

Suppose that 55% of all babies born in a particular hospital are boys. If 6 babies born in the hospital are randomly selected, what is the probability that fewer than 2 of them are boys?

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 =    6      
p = the probability of a success =    0.55      
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.069198047
          
Which is also          
          
P(fewer than   2   ) =    0.069198047 [ANSWER]