The statistical chances of someone committing larceny of $1k+ is in itself unlikely. The average citizen isn't a criminal.
Likewise, the statistical chances of someone being robbed of $1k+ is also low.
The typical theft sits at about a value of $1200 today. So, it's plausible that a criminal thief wouldn't take too long to amass a take of $6k. Combine this with an adolescent having no overhead/bills to pay, it's hardly impossible for an 18 year old to have $6k in this day ad age. Hell, my nephew is 14 and probably has more than that. Pretty sure he's not lifting cars after bedtime.