So, the premise states that more than half of the processors are still good. In that case, the proper thing to do would be to ask a single processor about all the other processors sequentially.
Suppose you have 10 processors. Since more than half are still good, we know that at least 6 of them are good, if not more. Essentially, we just need to ask one processor about all the others, until we find at least 5 of the same type. We ask processor 0:
Processor 0, is processor 1 good?
Processor 0, is processor 2 good?
etc., until we have five of the 5 of the same type. If those Processor 0 says those 5 are good, Processor 0 must also be good (and telling the truth). If Processor 0 says those 5 are bad, that isn’t possible, so Processor 0 is lying (and those 5 processors are actually good). So, we have at a minimum, N/2 questions needed to find a good processor. N-2 is a maximum.