Chapter CR, Problem 75E

Business: distribution of salaries. The salaries paid by a large corporation are normally distributed with a mean $\mu =\$75,000$ and a standard deviation $\sigma =\$6,000$.

a. Find the probability that a randomly chosen employee earns between $72,000 and $85,000 per year.

b. An executive of the corporation earns $90,000 per year. In what percentile of the salaries does this salary place him?

c. A new employee insists on a salary that is in the top 2% of salaries. What is the minimum salary that this employee would accept?