I am in the same situation as the original poster in that I too would like to construct 95% minimum convex polygons.
Mr. Patterson, I think you may be right in that this may be a clustering algorithm issue rather than the convex hull tool itself. The only example I can provide that better describes our question is this:
I have a distribution of animal movement points, i.e. lat/long (WGS 84), and I have just used the Minimum Bounding Geometry to construct a convex hull that encapsulates all of my points (see attached document). However, it is apparent that there are areas within my polygon that contain no points (empty) or are not near any other points, i.e. outliers. Essentially, this polygon represents 100% of my data points--this is what I believe the original poster meant by a 100% MCP. The downside of this method is that it produces a "home range", i.e. convex hull, that incorporates areas never used by the animals. Therefore, as a means to alleviate this downside, researchers disregard or remove the top 5% of the data points in hopes of reducing the impact of outliers or large data points. The new "home range," then, is 95% of the original 100%.
Is there a way to do this in ArcGIS?
Thanks in advance!