WageWeb is a service of HRPDI and provides compensation information on more than 170 benchmark positions in human resources. The October 2003 posting indicated that labor relation managers earn a mean annual salary of $87,700. Assume that annual salaries are normally distributed and have a standard deviation of $9400. (Give your answers correct to four decimal places.)
(a) What is the probability that a randomly selected labor relation manager earned more than $105,200 in 2003?
(b) A sample of 29 labor relation managers is taken, and annual salaries are reported. What is the probability that the sample mean annual salary falls between $86,000 and $88,500?