What kind of 'faith' justifies or imputes righteousness to a sinner as per the teachings of the Bible?

Protestant Christians in general believe that 'faith' makes a person righteous. The Letter to Hebrews chapter 11 in the N.T. talks about faith at length with specific examples. But what kind of 'faith' in 'what' can actually make a sinner justified or righteous as per the teachings of the Bible?