It's an easy stereotype to make. More Jews end up as professionals (lawyers, doctors, accountants) than businessmen, though. ;)
You tend to find Jews all over doing all sorts of things, despite small numbers (I think there's only 13 million left in all the world). All parts of the political spectrum, all occupations and all over the world. My family, for example, has a large number of doctors, lawyers and soldiers (with, it seems, a particular aptitude for officers in field intelligence, and heavy weapon deployment)
I grew up in the South, a land renowned for prejudice, and attended schools which drew students for all over the city, rich and poor. I was aware than many of my friends were Jews only years later when traveled beyond my home environment and started to realize that certain names frequently indicated the person was a Jew. As I reflected on the people I knew in school I realized many were Jews and none were poor, reflecting their families livelihood. You are correct in they were a mixture of doctors, lawyers, and merchants.
The amusing thing about my memories is that I never viewed them through a prism of stereotype because I didn't know they were Jews. They were all just like the rest of us. Although in retrospect, a few did fit the stereotype, even if I didn't know it, and none of us reacted to them as such.