The United Earth Space Probe Agency launched the first warp capable probe (Friendship 1) in 2067, which means deep space exploration had been going on for 198 years when "Where No Man Has Gone Before" took place. With that in mind my guess would be somewhere around 10%.
"Now, I am become Death, the destroyer of worlds." J. Robert Oppenheimer

It depends on what they mean by "explored." If it means just looking at stars and such through telescopes, the figure might be more. If it means physically going to these places, and studying them in depth, 17% comes off more impressive. In fact, it comes off as unbelievable. Because that means they have explored roughly 17 Billion stars!!! I'm calling bulls#it on that.