I have a 2 story house. Is it normal to hear water draining from anywhere in the house, upstairs or downstairs, in the upsatirs master bathtub drain?

It depends! What material are your drainage pipes? We get more complaints like yours from plastic pipes such as PVC or ABS but hardly any from cast iron.
Soooo, what do you have? Cheers, Tom

Hey Tom,
The pipes are plastic

It seems that plastic pipes will be noisier then cast iron. About the only way I know to quite them down would be to open up the wall and pack insulation around the pipes. That isn't much help but it's the best I can do. Regards, Tom

I suspect you have no trap installed on that tub. Investigate and let us know what you've found out... Back to you... Milo