Question: how do I setup/plot this probability distribution

How do I setup/plot this probability

As a thought example, time waiting in a line at cash register.  Let's say 40% of the time you are waiting for ~1 minute while 35% of the time you are served immediately and the rest of the time trailing off waiting up to 15 minutes.

Is this is like a skewed normal distribution?  and how could I set it up?  And then how can I randomly generate some values from this distribution?

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