Suppose I'm in line at a bank. There are 4 bank tellers, and 12 people in line in front of me. All the tellers are idle in the beginning so the first 4 customers get processed immediately. Each customer takes a random amount of time to be processed, with time drawn from a normal distribution with mean 10 minutes and standard deviation 2 minutes. How long should I expect to wait before I get to a teller?

I coded up a simulation in R and found that in this case, the distribution of wait time has mean 26.6 and standard deviation 2.2. Is there any way to solve this analytically? I'm not very well-versed in queueing theory, so any references would be appreciated.

*Edit: If changing the model in some way makes it easier (eg: exponential rather than normal distribution), then you are allowed to do so.*