The probability that a car will have a flat tire while drivi

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00004. Use the Poisson distribution to approximate the probability that among 11,000 cars passing through this tunnel, at most two will have a flat tire

Solution

The mean here is

mean = np = 11000*0.00004 = 0.44

Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    0.44      
          
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.989755172 [ANSWER]