Final answer:
A peripheral membrane protein synthesized within the ER lumen is likely to end up on the outside of the plasma membrane, serving functions in signaling, adhesion, or interactions with the environment.
Step-by-step explanation:
When a peripheral membrane protein is synthesized within the lumen of the rough endoplasmic reticulum (RER), its destination depends on the protein's function and the cellular machinery. Such proteins, once synthesized, are transported to the Golgi apparatus via transport vesicles. As they travel from the RER to the Golgi, and eventually to their final destination, these proteins can become part of the plasma membrane, be secreted into the extracellular space, or end up in other organelles. If a peripheral membrane protein that was synthesized in the ER lumen is to become part of the plasma membrane, it will most likely end up on the outside of the plasma membrane once the vesicle fuses with the cell membrane. This external positioning typically relates to the protein's functional role in cell signaling, cell adhesion, or interaction with the cell's external environment.