Suppose we are interested in the Annual Salary of Electronics Associated, Inc. (EAI) managers and we find that for a sample of n = 30 managers, there was 0.5034 probability of obtaining a sample mean within $500 of the population mean (see the figure below). For parts (a) and (b), let the population mean be 51,800 and = 4,000. (Round your answers to four decimal places.)

a) What is the probability that x is within $500 of the population mean if a sample of size 40 is used?