If a distribution has the property that the probability does not depend on any previous values, and is a rate, then Poisson is probably a good way to model it. In this case, that seems relatively fair - people are not less likely to show up if there are fewer or more people that showed up in the past.
The parameter you need depends on the rate. The rate is given as 120/hour. If you want the rate per minute, you can simply divide by 60, since the distribution can scale to any given time scale.
The mean value is simply the expected number of people, 120 in any given hour, or 2 per minute. To turn this into the Poisson distribution, we use the fact that the rate is the same as the distribution parameter. You can then evaluate the Poisson distribution to find the answer to your question.