Adding a bathroom in a 60s house in Cartersville, Georgia

[Gilles Guezille]

We just bought a large 3 bed 1 bath house on septic and fed by a well. We are adding a second bath to be the master bath, with a tub, toilet, and dual sink.
The existing bath is on the opposite side of the house and has its own stack.
I am planning on using a 2' pipe for venting and expanding to 4" just below the roof. Temps vary from 95F in summer to 25F in winter. Will this pass inspection, or do I need to start with a 3" vent pipe?

 

[Terry]

Normally a tub will vent with 1.5" and a full bathroom with 2"
Some places upsize the vents through the roof for frost. I'm in Seattle so it isn't an issue.