Customers arrive at a department store checkout counter according to a Poisson distribution with mean of 7 per hour. In a given 2 hour period, what is the probability that 20 or more customers will arrive at the counter?

I know I can solve it if I let the mean equal to 14 then solve for . But what I'm wondering is how would you go about solving this type of problem if you were to compute it using the moment generating function; which would also seem quicker and less tedious?