A binomial experiment is conducted with the given parameters

A binomial experiment is conducted with the given parameters. Compute the probability of X successes in the n independent trials of the experiment . n=11, p=0.3, x is less than or equal to 11

Solution

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    11      
p = the probability of a success =    0.3      
x = the maximum number of successes =    11      
          
Then the cumulative probability is          
          
P(at most   11   ) =    1 [ANSWER]

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Note that this is so because the \"at most 11\" is basically all possible values of x. Hence, it is a sure event.