# Risk Pooling Assignment

**Topics:**Normal distribution, Probability theory, Variance

**Pages:**1 (356 words)

**Published:**December 1, 2012

This assignment is designed to help you understand the concept of risk pooling. You are the CRO (i.e., Chief Risk Officer) of a manufacturing firm. The CEO asks you to design a risk management program for workplace injuries and says that she is willing to establish an internal risk management program (e.g., a self-insurance program) if with a 95% confidence, your firm will not have more injuries than 125% of the expected value. You tell the CEO that you need to assess if your firm has enough number of employees in order to establish such a program, and then takes on the task to find out. 1. Why did you tell the CEO that you need a certain minimum number of employees in order to establish this program?

2. What is the minimum number of employees that you need to have participating in this program? (Your answer should be a number, like “100” employees)

To answer question 2, you will need the following information: 1) Historical data shows that the number of injuries has been 10% of the number of employees in a given year. 2) The number of workplace injuries, X, typically follows a Poisson distribution with a parameter λ, where E(X) = λ and Variance(X) = λ. 3) We can reasonably approximate the Poisson distribution via a Normal distribution, with the same expected value and variance (according to Central Limit Theorem, for which you don’t need to know the details). 4) You will also need to use the critical value for the standard Normal distribution (i.e., z-score) associated with the 95% confidence interval. You can look it up in a z-table in any statistics book or online. Hint: Once you understand the question, the calculation should be very simple and only contain a few steps at most. If...

Please join StudyMode to read the full document