Linda McMahon, whose résumé mainly rests on running World Wrestling Entertainment, has faced questions for years over whether she is suitable for important education posts.

Allegations surrounding the company under their management included promoting steroids, a culture of rampant sexual harassment, intimidation and assault. There have been several out-of-court settlements involving the company or Mr. McMahon personally.

Most recently, a lawsuit filed in October accused the McMahons of willfully ignoring the sexual abuse of young boys by a W.W.E. ringside announcer, echoing claims made years ago.