A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 5 inches. A random sample of 41 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)

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