How do I create a shapefile of self-defined zones, using clusters of zip codes (ArcGIS)?

I have 6 zones in the United States that I defined by clustering all US zip codes. I now need a shapefile that depicts each of these zones in a different color. Here is an illustration of what I would like the map to look like:

What I am working with: A dataset containing every US zip code, their approx Long and Lat, and their zone designation. I have access to ArcGis 10. My knowledge of the software is limited, but I am a quick learner!

Ideally, what I would end up with is a single shapefile with each of the zones in a different color. The point of this is to use that shapefile in an app, which will project points onto a map of the US. That part I can do, I just need to user to be able to see which zone the point is in.