When presented with only circumstantial evidence, a juror tends to decide a case according to his or her gut instinct, which are not formally
sanctioned or prohibited means of reaching a verdict.
(A) which are not formally
(B) which are not a formally
(C) which is not a formally
(D) which is formally not a
(E) which is not formally
First split happens with regards to subject-verb agreement. The subject is "instinct." It is singular.
So eliminate (A) and (B).
Second split (and last split) has something to do with logical construction and proper modifier (modification).
As such I go with (C) as it grasps the entire idea of what the author is trying to say.
Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt