You must tell us how do you use your phone.
If you are using your phone for 3 hours for playing high end games or surfing internet with 3g connection probably is normal.
If battery drops in standby there is an issue
Check also if your phone overheats in idle (standby)
You can also load android in safe mode (with only stock apps) and check battery life
- Turn off the device.
- Press and hold down the power key until the phone vibrates.
- Wait until the Xperia™ logotype disappears.
- Press and hold the volume down key. The device then restarts in safe mode.
- To exit safe mode, restart the device.
