A manufacturing process is designed to produce bolts with a $0.5$ -inch diameter. Once each day, a random sample of 36 bolts is selected and the bolt diameters are recorded. If the resulting sample mean is less than $0.49$ inches or greater than $0.51$ inches, the process is shut down for adjustment. The standard deviation for diameter is $0.02$ inches. What is the probability that the manufacturing line will be shut down unnecessarily? (Hint: Find the probability of observing an $\bar{x}$ in the shutdown range when the true process mean really is $0.5$ inches.)