The movie "2012" is based on several doomsday prophecies as disparate as the Mayan calendar, numerological constructions, and messages from extraterrestrial beings. As a rational thinking statistician, you decide to find out what proportion of the U.S. population actually believes in these prophecies. You take a randomly collected sample of 350 people and discover that 45 of them believe at least "somewhat" in the predictions. Construct a 95% confidence interval for the proportion of U.S. population who believe at least "somewhat" in doomsday prophecies. (Show your work or formula.). Interpret the interval.