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 recoreded.
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?