2-4 weeks of daily study shouldn't be close to enough on average, not even remotely in the ballpark, assuming you are talking about a rank beginner.
What do you think would be a better estimate?
I dunno, some people simply have no talent and will have major trouble with even a lot of training. I mean there are lots of kids who study for years and never get above 1300-1500. The same is true of many adults. Of course most adults just assume it won't be the case with them. Also it takes a lot of practice playing, I think it takes more time. Like 2-3 hours of study per day over a longer period of time would be more beneficial.