Former General Electric chief Jack Welch, is an enthusiastic advocate of forced ranking, calling it the vitality curve. Forced ranking is seen by some as a handy grading tool for creating a high-performing culture. In this problem you will examine some of the implications of forced ranking. You are trying to build a high-performing sales force. However, it is hard to ascertain the quality of a sales agent without employing them for some period. You decide on a policy of hiring a large number of agents for one year. If an agent generates a revenue that puts them in the top 2.5% of all agents, you will retain them. Otherwise, you will let them go. Extreme, yes, but you want a very high-performing sales team. The revenue that an agent brings in varies from one year to the next, but not according to the same distribution for every agent; it so happens that sales agents are of two kinds. Good sales agents generate an annual revenue that is normally distributed with a mean of $120K and standard deviation $5K. Bad sales agents generate an annual revenue that is normally distributed with a mean of $100K and standard deviation $20K. Assume your initial pool of sales agents is split 50-50 between good and bad.
1. You have decided to find the revenue cutoff which results in 2.5% of all agents being retained. Using Excel, create a table which shows, for each possible cutoff from $115,000 to $140,000 in $1,000 increments,
(1) The fraction of good agents who make the cutoff,
(2) The fraction of bad agents who make the cutoff,
(3) The fraction of all agents who make the cutoff,
(4) Of those who make the cutoff, the fraction who are good. Include the table in your answers. What cutoff in this table comes closest to your goal of 2.5% retention?
2. If you use the cutoff you found in (a), what percentage of the agents you retain will be