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 2 inches.
A random sample of 36 fish is taken from the tank.
Let x bar be the mean sample length of these fish. What is the probability that x bar is within 0.5 inch of the claimed population mean?
Show all work. Then, provide a brief step by step explanation of process.