A noise floor of -118dB isn't just normal...it's actually very good.
I suspect you have a few things going on here. First, recording extremely low (-40dBFS) doesn't reduce your noise level if you then have to normalise later. When you add 30 or 40 dB of level to your voice, you're adding exactly the same amount to your noise. You should be recording with your voice peaking at between -14 and -10dBFS which is equivalent to between PPM5 and PPM6 if you're used to European style PPM meters. You need a microphone and pre-amp combination that lets you record at these levels without noticeable noise.
I've never used the interface or mic you have so don't know what you should be able to expect. However, after listening to your sample, I suspect that it might be a combination of your mic needing a better pre-amp to get sufficient level and the Presonus becoming noisy when you turn the gain up sufficiently for the microphone. Perhaps somebody who knows the Audiobox will pop in and let you know if this is normal or if you have a faulty unit.
The solution? An interface with better (i.e. quieter) mic pre amps or a mic with a higher output level--or both. As you say, for voice work you need a better S/N than for music. However, I have to say that, based on your sample, you also have some room noise/acoustic issues on top of the electronic hiss.
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-Tyrion Lannister (and Bobbsy)