That's hard to say as it's not simply a matter of having ringing ears or not. Suffice to say most people will hear sound if they are in a quiet room. Tinnitus is what you have if this sound bothers you, possibly because it's louder than the sounds other people have in their heads. However, habituation is an important factor in this. Reacting in a negative way to the sound may worsen it while "ignoring" the sound over time will potentially reduce it's strength back to levels where it's normally ignored by the brain.
Basically, sound is picked up by sensory cells in the ears and then transmitted through the limbic system in the brain where, to illustrate, you could say the sound is given a tag indicating it's importance - f.ex if it's a dangerous "important" sound or a harmless "non-important" sound. The sound from the refrigerator can be just as high as the ringing in your ears, but most people don't notice this sort of stuff because the sound is not important. Thus, the brain tries to filter it out. People who have a starting annoyance with ringing in their ears should realize the importance of this. Basically, ringing in your ears can be habituated and you won't mostly won't notice it unless you're someplace quiet.
Anyone who believe they may have starting tinnitus need to read about TRT, Tinnitus Retraining Therapy!
The Tinnitus and Hyperacusis Centre: home of TRT