Although faculty salaries at colleges and universities in the United States continue to rise, they do not always keep pace with the cost of living and with salaries in the private sector. In 2010, the National Center for Educational Statistics indicated that the average salary for Assistant Professors at public 4-year colleges was $63,441. Suppose that these salaries are normally distributed with a standard deviation of $4000.
a. What proportion of assistant professors at public 4-year colleges will have salaries less than $55,000?
b. What proportion of these professors will have salaries between $55,000 and $65,000?