Who determines what is normal?

No single person determines it, but rather mostly past actions and a few recent large events.

If we had to make it a math formula, I'd say something like

norm(t) = norm(t-1)0.95 + recentBehavior0.05

Where norm is the set of what's normal, t is a time period (year, month, etc)

I've been poking around in mental health stuff a lot lately so I'm going to come from that angle. "Normal" is a group descriptor. People get caught up comparing themselves to the group average (or worse group 'best') and it causes a ton of mental anguish. No individual meets every norm for a group, and if someone did, that would be pretty abnormal! Since I strive to be a solutions oriented individual, I'm gonna ramble on a bit. In my humble experience, a vastly superior metric to compare oneself to would be 'how are you doing in this moment vs. how would your past self have handled the current situation'. For me, I already had a mechanic for this - "cringe memories". I frequently would catch myself thinking back to situations where I'd performed sub-optimally and at times experience crippling emotions cringing from the memory. Then some kind soul on the interwebz pointed out that the only way I could look back on those memories and regret the behavior was if I had grown since that moment and come to see it for what it was - a (sometimes vastly) less skillful attempt to handle a challenging situation. It's been a journey but I can now catch myself cringeing and switch the narrative to thanking past me for working so hard to get to a place where my previous actions seem so unskillful.

First, I have never felt normal in my life, so this ay be my bias speaking, but I think normal an illusion (or delusion). When we say something is normal, it is a story we tell ourselves about acceptable behavior. The illusion lies in our limited experience. People's life experience, upbringing, culture, and viewpoint is so diverse that the reality of each person's life is utterly unique. It is our inability to experience all those details that creates the illusion of sameness or normality.

The broader we draw the category, the easier it is to call something normal, but when we look at the details, it becomes clear that there is no consensus behavior. We can say, "it is normal to eat". But "it is normal to eat three meals a day" is already unlikely to include everyone you know.

The narrower we define the in group, the easier it is to call something normal, but it is likely to be something that directly relates to the purpose of that in group. We can say, "It is normal for everyone in my family to eat three meals a day". But we can't say, "it is normal for everyone in my family to go to school".

I also think normal requires deviation -- something not normal. If it's truly a universal experience, we might not even have a word for it because there's nothing to distinguish it. There is an SMBC comic (I think, I can't find it now) that points out there's no word for "keeping your liver inside your body" because that is the universal experience.

In my field, a normal coworker needs 1-1,5 years of training before they can do the job on their own most of the time if you have prior experience. If not, add another six months. If they need just six months you know that they are either completely over qualified or (far more likely) pretend to know, and you'll have to triple check everything as most likely they are a disaster.

Who determines this? Many years of experience and talking to countless new coworkers in that time.