Standarization

Hello everyone. I have this dataset that looks like this. I want to create a variable that standarizes the variable "promp08" using the variables "recinto" and "carrera". See, this is a ficticious database about people from a university, and the goal is to create a variable that standarizes the average grade for every student for every major and in every hearquarter of the university, i just don't know how to generate a variable that computes the mean and standard deviation for "promp08" for each major. I'm using version 14 of stata and i'll be thankfull for any help that ypu can give me! Array