A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is $800,000, and the standard deviation is $300,000. A random sample of 100 agents is selected, and the value of the properties they sold in a year is recorded.
a. What is the standard error of the sample mean?
b. What is the probability that the sample mean exceeds $825,000?
c. What is the probability that the sample mean exceeds $780,000?
d. What is the probability that the sample mean is between $790,000 and $820,000?