A telecommunication station is designed to receive a maximum

A telecommunication station is designed to receive a maximum of 8 calls per second. If the number of calls to the station is modeled as a Poisson random variable with a mean of 10 calls per second, what is the probability that the number of calls will exceed the maximum design constraint of the station? Round your answers to four decimal places (e.g. 98.7654).

Solution

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    10      
          
x = our critical value of successes =    8      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   8   ) =    0.332819679
          
Thus, the probability of at least   9   successes is  
          
P(more than   8   ) =    0.667180321 [ANSWER]