Check if Voltage is in a certain range
Zener is actually a good idea. Later you can replace it with voltage reference IC for better accuracy, but zener is just fine for your application.

You need two low voltage comparators, each will have a reference voltage set by a zener (with resistor in series! and a capacitor for cleaner signal...) and each will have a voltage divider (two resistors) with your input voltage on top. And- some basic logic on comparators outputs.