The skull of Tyrannosaurus rex (better known as T. rex) on display in the Orton Museum is a cast of a specimen in the American Museum of Natural History (AMNH 5027). The original was collected from the Hell Creek Formation (Cretaceous) of Big Dry Creek, Montana, by the famous fossil collector Barnum Brown in 1908. It was the first T. rex to be unearthed with a complete skull. Here is a link to more information about this important specimen.
Knowledge about T. rex has improved substantially since the early 1900s. This interesting article explains many of those changes in our information, and in the way that T. rex skeletons have been displayed in museums.