How to use possion to estimate arrival time (generate random intergers)?

In my assignment, I'm supposed to use a distribution curve to describe how many minutes will the employee come to work in advanced or later than the planed start time.

I decided to use Poisson distribution to solve my case. However, I don't know how should I assign the parameter to the Poisson function. I want my x-axis is from 0 to 60 minute (integer). The peak of the curve should be show up when x is 15. Should I just assign the lambda as 15?

I don't know if it's correct to use Poisson distribution to estimate the arrival time, and also don't know, if Poisson is correct, then should I just let the lambda be 15 and that's it, how can I set up a specific range (0, 60)?