In the EAI sampling problem, the population mean is $71,800 and the population standard deviation is $4000. For n=30 , there is a 0.5064 probability of obtaining a sample mean within +/- $500 of the population mean. Use z-table.

a. What is the probability that x is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?

b. Answer part (a) for a sample of size 120 (to 4 decimals).