I am not sure if your suggestion is correct? 11.9V is good voltage, but need to make sure you have a load on the battery when the measurement is being taken
Measuring voltage is a tricky task. You need a load connect to a battery in order to get a accuracy reading. If there is no load, you always get the good voltage. When the load is connected to a battery, the measurement will tell the condition of the battery. This simply when there is a load, if the bettery is weak, the battery will no longer able to maintain the 12.0V.
Try this, turn the key on, without the car running. Turn on the headlight and the heater and fan (equivalent to putting the load on the battery). Then measure the voltage at the battery's terminals. A good battery will measure anywhere from 10.5 to 13.0V.