The average annual salary for federal government employees in Indiana is $41,979 (The World Almanac, 2001). Use this figure as the population mean and assume the population standard deviation is = $5000. Suppose that a random sample of 50 federal government employees will be selected from the population.

a. What is the value of the standard error of the mean? b. What is the probability that the sample mean will be more than $41,979? c. What is the probability the sample mean will be within $1000 of the population mean? d. How would the probability in part (c) change if the sample size were increased to 100?