The average diameter of sand dollars on a certain island is 4.50 centimeters with a standard deviation of 1.00 centimeters.

The average diameter of sand dollars on a certain island is 4.50 centimeters with a standard deviation of 1.00 centimeters. If 16 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 4.20 centimeters. Assume that the variable is normally distributed.