Is there research on how long it takes an "average" person to memorize a piece of information?
Say a word or a license plate. Something along the lines of: "Given a license plate, and 100 repetitions of said license plate, 95% of all people are expected to remember it in 24 hours, 80% in 48 hours, etc"
Yes. A lot.
A possible place to get started is the wiki page for Ebbinghaus, skip to "Contributions to memory".
Ebbinghaus's work is kind of dated, like 1885 kind of dated, but the point is the discussion there will give you some handy search terms.
In particular, I think "forgetting curve / learning curve" on google scholar will get you where you're going faster than searching for 'memory'.
The question seems to suggest you're most interested in individual differences? Usually people study aggregates, because individuals are so noisy (Ebbinghaus famously did it with one participant, ramping up the number of trials instead, but his methodology wouldn't really fly today). One study that argues against that and does drill down to individuals is Avarell & Heathcote (2011). Their stimuli are short words. Not sure if that's quite what you're after, but might be worth a shot?
If basic research into memory is what you want though there's an embarrassment of riches out there. Good luck!
Averell, L., & Heathcote, A. (2011). The form of the forgetting curve and the fate of memories. Journal of Mathematical Psychology, 55(1), 25-35.
