A manufacturer makes integrated circuits that each have a resistance layer with a target thickness of 200 units. A circuit won't work well if this thickness varies too much from the target value. These thickness measurements are approximately normally distributed with a mean of 200 units and a standard deviation of 12 units. An inspector has been tasked with randomly selecting circuits and calculating their measurements. A random sample of 16 measurements is selected for a quality inspection. What is the probability that the mean thickness in these 16 measurements is farther than 3 units away from the target value?