Final answer:
The underlined part of the sentence functions as a noun clause, serving as the object of the verb in the sentence.
Step-by-step explanation:
The underlined part of the sentence "No one believed that Peter would actually jump" is a noun clause. A noun clause is a dependent clause that can function as a noun within a sentence; hence, it can serve as the subject, object, or the complement of a verb or preposition. In this case, "that Peter would actually jump" serves as the object of the verb "believed" and therefore, the correct answer is (E) noun clause.