# Operations Risk Management

1. The Normal Distribution . There are 6,000 households in the town of Rockbottom, MA. The annual household incomes are normally distributed with a mean of \$70,000 and a standard deviation of \$20,000.

a. Approximately how many households in Rockbottom have annual incomes greater than \$130,000 ? b. Approximately how many households in Rockbottom have annual incomes less than \$30,000 ?

2. Your elderly uncle Boris has died from eating too much pepperoni and has left you \$10,000. You may invest it either in a CD that pays 4.5% for sure or in the Fly-by-Night Mutual Fund whose returns and probabilities you have assessed as:

Probability of Up 25% Probability of Up 10% Probability of Down 10% 25% 50% 25%

a. If you are risk-neutral, what should you do and what is the EMV? b. If you are risk-averse and have a risk tolerance of \$1,500, what should you do and what is the risk-adjusted value? (Do both manually, and using Ptree.) c. You have a friend, Jerry S., who is a stockbroker. In his 30 years of brokering stocks, he has never been wrong! If Jerry says it will go up 25%, you can take that to the bank. Jerry is willing to assess the Fly-by-Night Fund for you and to provide the probabilities of the fund going up 25%, up 10%, and down 10%, for a fee of \$500. (Yes, he’s your friend, but business is business.) a) If you are risk-neutral, what should you do and what is the EMV? b) If you are risk-averse and retain a Risk Tolerance of \$1,500, what should you do and what’s the Risk-Adjusted Value? (Do just using Ptree.)

3. The Binomial Distribution In the Hard-Knox High School (2500 students), 18% of the students smoke cigarettes. A) If 2 are selected at random, use a Venn diagram with 2 circles; 1 representing the probability that the first student smokes and 1 representing the probability that the other student smokes. Determine the probability that at least 1 of them smokes cigarettes. B) Repeat the above analysis when 3 students are selected at random. Note: These trials would be independent given the large population of students.