Determine the distribution of charges on the sphere if it is made of non-conducting plastic.

If the sphere is made of a non-conducting material, charges can't distribute freely over its surface or volume. In non-conducting material bodies, charges can be transported from a molecule to another nearest to it. Therefore if you rub an object with a positive charge with this sphere made of non-conducting plastic, the object will rip some negative charges (electrons) of that zone of the sphere. Therefore that zone will get a superficial positive charge density, but the non-affected zone of the sphere will keep having a null charge density.