I fly the J-31!

Capt. Doug wrote:
I had the opportunity to fly a Jetstream 31 recently.

Hi Doug, enjoyed reading this. One question:

Along the way, the TCAS alarm went off. That's one of those things that sits
you up right away with wide open eyes searching frantically for the other
plane. Apparently, the other plane was well below us but without Mode C. The
TCAS unit doesn't know the altitude, so we get a warning. If the other plane
had an operating Mode C, the TCAS unit would have determined there was no
threat.

How common is this? Do planes in the flight levels commonly get TCAS
warnings about planes w/out Mode C who are well below them? Is there
any distance below you where TCAS will be able to determine that the
other plane isn't a threat sans Mode C?

IOW if a plane w/out mode C is at 9,500 will you get a TCAS in the
flight levels?

Thanks,
Sydney