What is the probability that a customer waits for lesser than 3 minutes?

The rate of service is exponential and the service rate is 12 customers served per hour. The arrival of customers is in a Poisson distribution at the rate of 30 per hour. There are 3 servers and the average waiting time is 7 minutes. How would I go about doing this? Could really use some help!

Edit - I've also calculated the probability that an arriving customer has to wait as 0.7. Not sure how to calculate the probability regarding waiting time though.

What you want is not the total time a customer spends in the system, but just in the line. Do you know the formula for the queue waiting time $\mathcal{W_q}$ distribution of an M/M/3 queue? Its a pretty common formula in queue theory textbooks. Its cumbersome to write, so ill jsut link you to it, see Slide 35 of this ppt. And p.13 of this
• See the links I sent you, $P(\mathcal{W_q}>t)$ is in there. Should help you out a lot. – user76844 Nov 4 '13 at 15:46