Poisson process - expected number of arrivals in time interval I came across this question and can't figure out if I'm missing something or if the answer is just "$3$". Can anyone clarify?

Question:

"The number of people arriving at a certain "take away" drive-through restaurant follows a Poisson process with mean one. Suppose that the waiters can only process three orders in any given four minute interval, and assume that they can process these orders instantaneously. What is the expected number of people that will actually leave the drive through restaurant with their orders filled, in any given four minute interval?"

I'm assuming by "mean", the question means $\lambda=1$ so then $\mathrm{E}[N(4)]= \lambda \cdot 4 = 4$. Then of those $4$, only $3$ can have their orders filled.

The only alternative I can think is that by "mean" the question means $\mathrm{E}[N(t)] = 1$, but then only one person is served in any time interval, even if that interval is infinite.
hint

You want the mean number of customers served. There will either be $0,1,2$ or $3$ depending on how many arrive (it's $3$ if three or more arrive). You know the distribution of how many arrive is Poisson with mean $4$. So you can calculate the expected value. It will be less than $3$.
You first assumption is right. A Poisson process with $\lambda = 1$.