Dear Ms. Soholt,
According to this history of the North Dakota State Hospital for the Insane, it was opened in 1885 and was renamed in 1951 as the North Dakota State Hospital. Your plate could have been produced anytime from the 1890s to the 1910s, perhaps. As to the "The Fair" reference on the plate, this article says that the Stutsman County Fair (of which Jamestown is the seat) dates back to 1897.
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