According to the Organisation for Economic Cooperation and Development (OECD), adults in the United States worked an average of 1,783 hours in 2016. Assume the population standard deviation is 400 hours and that a random sample of 50 U.S. adults was selected.

a. Calculate the standard error of the mean.

b. What is the probability that the sample mean will be more than 1,800 hours?

c. What is the probability that the sample mean will be between 1,750 and 1,780 hours?

d. Would a sample mean of 1,825 hours support the claim made by the OECD?

e. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is 1,783 hours.