Customers use an automatic teller machine at an average rate

Customers use an automatic teller machine at an average rate of 5 per hour.What is the probability that exactly 12 will use the machine in the next hour? (Hint: Since the average/mean is given, solve using the Poisson).

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where     
= parameter of the distribution.        
x = is the number of independent trials
P( X = 12 ) = e ^-5 * 5^12 / 12! = 0.0034