Yes, abstractly, of course. On the other hand, this sort of distribution is usually gaussian (a whole bunch of average drivers, and a few specially good and bad ones), and it is true that 80% of the people can't be above average if they are samples from a well-behaved distribution (with controlled skewness, and in the correct scale, etc)
Gaussians don't work very well when the typical value is near one of the bounds. For example say 3/4 of drivers don't eat, apply makeup, talk on the phone, etc, while driving, and generally pay attention to the road; that sort of attentiveness is probably most of what makes a good driver, so you'd have the majority of people being near one extreme of the possible range and get a rather one-sided distribution.
No. That distributions are commonly Gaussian is some quasi-mystical nonsense left over from 'psychometrics' about 100 years ago.
The most common way to get a Gaussian distribution is from the central limit theorem, and it's much worse than clumsy to argue its assumptions here.
Gaussian needs MUCH more than your "a whole bunch of average drivers, and a few specially good and bad ones".
Your "well-behaved" is asking far too much for practice or reality. Gaussian isn't "well-behaved"; from Melon in 'Back to School', it's "fantasy land". E.g., there's no reason to believe that can have your "controlled skewness".
On your "scale", sure, if know the distribution and if it is absolutely continuous with respect to Lebesgue measure, then can pick a scale that maintains order and yields Gaussian. The educational testing people love to do this. It's quasi-religion. And we collect taxes to pay them for that?
Yes, for stock market data can argue that changes in price each 15 seconds are independent and identically distributed with finite mean and variance so that the central limit theorem applies so that the change in price from noon today to noon next week will be Gaussian. Of course there are traders driving Ferraris laughing at that.
Do yourself a favor: For real data, assume mean and variance exist and are finite, but without a really careful appeal the the central limit theorem dumpster Gaussian. For multivariate data, don't even think about Gaussian.
Uh, some diffusion processes in physics might give you 3D Gaussian quite accurately.
To be pedantic, most people usually mean "median" (or a robust estimation of the mean without considering outliers) by average, and in samples from a continuous distribution it is necessarily true that ~50% are above/below the median.
