The other replies discuss how to create copies of vector data layers in a new coordinate system. You can also change the map's coordinate system in ArcMap. Because I think you've received an mxd, rather than a mdx, file.
In ArcMap, open the data frame properties by right-clicking Layers in the table of contents. Select the Coordinate System tab. The current coordinate system will be listed, and you can use the directory tree to browse to the coordinate system that you want to use. If there's a search box, and you know the well-known ID of the State Plane zone that you want to use, you can search on that.
Melita