Salaries for various positions can vary significantly, depending on whether or not the company is in the public or private sector. The U. S. Department of Labor posted the
2007 mean salary for human resource managers employed by the federal government
as $76,503. Assume the annual salaries for this type of job are normally distributed
and have a standard deviation of $8850.

a) What is the probability that a randomly selected
human resource manager received over $100,000
in 2007?
b) A sample of 20 human resource managers is taken
and annual salaries are reported. What is the
probability that the sample mean annual salary
falls between $70,000 and $80,000?