Normal Voltage Reading?

I ended up with an X2 (Northstar) AGM Group 34/78, 880 CCA & 68AH (4-year warranty).

When I turn off the Jeep and wait a few minutes the voltage settles to 12.7. What should I expect it to be by morning with that size battery—maybe a 0.1v decrease? At that rate it could last maybe two weeks without moving.
 
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i just replaced my battery after it sitting for a while, got her to start, shell stay running no prob but the battery gage drops to 0 after a few of idle or driving. i tested the battery volts after driving for a while and its at 11;56 did the test on the alternator its reading 11;15 what do yall think ? im stumped
 
The problem is more than likely a bad alternator, but also could be the ECU not controlling the charging properly.
Remove the three 32 pin harness connectors from the ECU and look for oxidation on the pins and clips; reseat the harness connectors.
If the problem remains; remove the alternator and have it tested at a local auto parts store.