1. ## Poisson Distribution

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 $\displaystyle 1-(P[Y<20]) = 1-(P[Y=0]+...+P[Y=19])$. 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?

2. Originally Posted by lllll
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 $\displaystyle 1-(P[Y<20]) = 1-(P[Y=0]+...+P[Y=19])$. 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?
Calculating probabilities is not one of the uses of the moment generating function.