That's why all three (plugs, over the ears, and a suppressor) should be used in conjunction for best results.
General industry standards that I'm used to are as follows:
-sustained noise over 84dB should use plugs/muffs
-sustained noise over 104dB should use both plugs and muffs
-peak noise over 140dB should use both plugs and muffs, regardless of average sustained noise dB. If sustained noise is over 84 then start using additional mitigation measures such as sound dampeners, barriers, distance from noise generating object, etc.
That being said, if a suppressor brings peak noise down to ~135dB you should STILL be using double ear protection. But it's way better than bringing it down from 170dB.