The curve definitely has a high left distribution. Things are often very late, but are never more than a few minutes early.
For example, it can never be less than 40 minutes between the time I park in the offsite lot, and when I sit down at my departure gate. Maybe the mean time is 50 minutes, but it could be 90 minutes. 120 is unlikely enough that I don’t plan for it to take that long, because out of 20 trips it would only happen 1 time.
(Of course there are external factors that can change this, so if it was an extremely busy travel time, and the government was shut down, and there was construction on the route from the offsite lot to the terminal… 120 minutes might be into the meaty part of the probability curve.)
That all goes into the planning, and not wanting to resurrect the old “why are people late” thread, complicated and time dependent tasks will require additional compromises based on the importance of completing the task.
Some people, like my mom, can go way overboard the wrong way. She doesn’t want to fly, because it would require her getting to the airport 4 hours early, just to feel like she’s on time. I’ve known other people who feel like they’ve failed at travel if the plane isn’t boarding when they first walk up to the gate.
Both types need to adjust their expectations more inline with reality.
My only experience with trains is in Europe, and all the same rules apply, but instead of being there 2 hours before departure, maybe it’s only 10 minutes before departure. A much more pleasant system.
Even that can still need compromises. For example, leave 10 minutes extra early to make sure you catch the 8:52, because the next express isn’t until 9:52, and the non-express will cost you 30 minutes. So you’re spending 10 minutes as a hedge against losing 30. Still better than flying, where the option might be to spend an hour as a hedge against losing a day (and money).