The average number of cars going through a toll booth is 5 p

The average number of cars going through a toll booth is 5 per minute. If the booth can handle 12 cars per minute without forming a line. what is the probability there will e a line at the toll booth? P( x> 12)

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 =    5      
          
x = our critical value of successes =    12      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   12   ) =    0.997981148
          
Thus, the probability of at least   13   successes is  
          
P(more than   12   ) =    0.002018852 [ANSWER]