My personal philosophy on all software is…If you dont trust any of the connections being made then this signifies a total lack of trust for the software as a whole.

i find it odd that you trust avast enough to install it and yet you question the connections it makes which implies a slight suspicious nature in your character.

Avast is a globally recognised security solution and used by millions of people worldwide so its credentials are not up for questioning.
Just allow avast to give you top notch av protection and stop being paranoid about avast outbound connections.

Thanks.