Final answer:
The Signal Hypothesis explains that secretory proteins possess a signal peptide that directs them to the RER, where it is cleaved to form a mature polypeptide. A peripheral membrane protein synthesized within the ER lumen would end up on the outside of the plasma membrane.
Step-by-step explanation:
After observing that proteins in the ER were larger than those in their native locations, the Signal Hypothesis was formulated. According to this hypothesis, secretory proteins have extra amino acids at the amino-terminal end, known as a signal peptide, which directs the secretory polypeptide to the rough endoplasmic reticulum (RER). The signal peptide is cleaved off by a signal peptidase within the RER, resulting in a shorter mature polypeptide.
When considering the localization of a peripheral membrane protein synthesized inside the lumen of the ER, it would typically end up on the outside of the plasma membrane. The protein would initially be directed into the lumen of the RER, where it undergoes modifications, and then it would travel via transport vesicles to the plasma membrane, ultimately residing on the external surface.