Beyond the Boxscore did a nice piece on this. There is a lot of data and you're welcome to look at the entire entry here How Long Does It Take for Top Prospects to Succeed in the Majors? - Beyond the Box Score
The data they used was top prospects 1-40.
Conclusions
Prospects usually make you wait. They rarely have even league average seasons right away. Although it is unclear how much of this is because they are not yet average talent players, or because they are not given the opportunity to show how good they are over a full season of regular playing time.
Most top prospects (58.6%) blossom in their second or third major league season. But for any prospect, there’s a significant chance that he’ll blossom anywhere from his first to fifth season.
Top pitching prospects have their first league average MLB season a little earlier than position player prospects.
On average, you have to wait until a position player’s third season, after about 120 games and 440 PA for his first league average season.
On average, you have to wait until a pitcher’s second or third season, after about 33 games, 19 starts and 130 IP for his first league average season.
Age at first MLB call up is not a meaningful variable in how long it takes a top prospect to succeed in the majors.
Better prospects (by BA rank) succeed a little more quickly than lesser prospects, but the difference is not great.