What is the protein synthesis pathway in the cell?

A certain gene on a chromosome in the nucleus is transcribed, and the mRNA coding for the protein found on said gene moves to the rough endoplasmic reticulum where it enters a ribosome. The desired protein is synthesised by the ribosome and exits the endoplasmic reticulum to go to the Golgi apparatus. It is then modified and packaged into a vesicle which is in turn sent to the plasma membrane where the protein is ejected from the cell via exocytosis.