Learning Experience: 3



Formalized Decision-Making Using Climate Forecasts

Use contents of this packet as you feel appropriate. You are free to copy and use any of the material in this lesson plan.

Packet Contents

Decision Making Activity Lab

NOTE: there are two copies of the lab, one using fractions and one using decimals. Use the lab that is appropriate for your Students.

Blank Decision Trees - for use if development of other decision problems is used as homework

Decision Tree Problems

Decision Making Activity Lab

The next 4 pages are for students completing the lab using fractions.

Decision Making Activity Lab

In this activity, you will use your knowledge of the three ENSO phases, El Niño, La Niña, and Neutral, to help Joe Soccer make a decision about which league to join. Information you will need to help Joe soccer is the probability of the different precipitation levels given the different ENSO phases. This information is from Learning Module 4 for Bryan / College Station and is replicated in the following table.

| |Precipitation Level | |

|ENSO Phase |Below Normal |Near Normal |Above Normal |All Precipitation Levels |

|All Years |10/30=.333 |10/30=.333 |10/30=.333 |30/30=1 |

| |33.3% |33.3% |33.3% |100% |

|El Niño |1/9=.111 |2/9=.222 |6/9=.667 |9/30=.30 |

| |11.1% |22.2% |66.7% |30% |

|La Niña |6/11=.545 |4/11=.364 |1/11=.090 |11/30=.367 |

| |54.5% |36.4% |9% |36.7% |

|Neutral |3/10=.30 |4/10=.40 |3/10=.30 |10/30=.333 |

| |30% |40% |30% |33.3% |

You will also need the following information on the number of games played given each precipitation level.

|Summary of number of average number of games played by|

|league and precipitation level. |

| |League |

|Precipitation Level |Indoor |Outdoor |

|Below Normal |7 |10 |

|Normal |7 |8 |

|Above Normal |7 |5 |

1. Complete a decision tree for each ENSO phase. Hint: each phase will have a different number of years. Be sure to use the correct number of years for each phase and precipitation level. If using the decision tree handout, part of the El Niño decision tree is completed to help you get started.

ENSO Decision Trees by Phase

All Years El Niño Phase

Goal__________________________ Goal__________________________

La Niña Phase Neutral Phase

Goal_________________________ Goal_________________________

2. For each phase calculate the expected value for each decision. Recall the formula to calculate expected value is as follows. Hint: the expected value for the outdoor league and El Niño is given to help you get started.

[pic]

All Years

Indoor

Outdoor

El Niño Phase

Indoor

Outdoor

[pic]

La Niña Phase

Indoor

Outdoor

Neutral Phase

Indoor

Outdoor

3. What is the best decision for Joe to make given the ENSO phase is El Niño?

4. What is the best decision for Joe to make given the ENSO phase is La Niña?

5. What is the best decision for Joe to make given the ENSO phase is Neutral?

6. Why is the expected value for playing in the indoor league the same for each ENSO phase?

7. Why is the expected value for playing in the outdoor league the different for each ENSO phase?

Decision Making Activity Lab

The next 4 pages are for students completing the lab using decimals.

Decision Making Activity Lab

In this activity, you will use your knowledge of the three ENSO phases, El Niño, La Niña, and Neutral, to help Joe Soccer make a decision about which league to join. Information you will need to help Joe soccer is the probability of the different precipitation levels given the different ENSO phases. This information is from Learning Module 4 for Bryan / College Station and is replicated in the following table.

| |Precipitation Level | |

|ENSO Phase |Below Normal |Near Normal |Above Normal |All Precipitation Levels |

|All Years |10/30=.333 |10/30=.333 |10/30=.333 |30/30=1 |

| |33.3% |33.3% |33.3% |100% |

|El Niño |1/9=.111 |2/9=.222 |6/9=.667 |9/30=.30 |

| |11.1% |22.2% |66.7% |30% |

|La Niña |6/11=.545 |4/11=.364 |1/11=.090 |11/30=.367 |

| |54.5% |36.4% |9% |36.7% |

|Neutral |3/10=.30 |4/10=.40 |3/10=.30 |10/30=.333 |

| |30% |40% |30% |33.3% |

You will also need the following information on the number of games played given each precipitation level.

|Summary of number of average number of games played by|

|league and precipitation level. |

| |League |

|Precipitation Level |Indoor |Outdoor |

|Below Normal |7 |10 |

|Normal |7 |8 |

|Above Normal |7 |5 |

Hint: the number of games played depends on the precipitation level and not the ENSO phase. However, the ENSO does affect the probability of a particular precipitation level.

1. Complete a decision tree for each ENSO phase. Hint: each phase will have a different number of years. Be sure to use the correct number of years for each phase and precipitation level. If using the decision tree handout, part of the El Niño decision tree is completed to help you get started.

ENSO Decision Trees by Phase

All Years El Niño Phase

Goal__________________________ Goal__________________________

La Niña Phase Neutral Phase

Goal_________________________ Goal_________________________

2. For each phase calculate the expected value for each decision. Recall the formula to calculate expected value is as follows. Hint: the expected value for the outdoor league and El Niño is given to help you get started.

(probability of below normal precipitation * games) + (probability of near normal precipitation * games) + (probability of above normal precipitation * games)

All Years

Indoor

Outdoor

El Niño Phase

Indoor

Outdoor

[pic]

La Niña Phase

Indoor

Outdoor

Neutral Phase

Indoor

Outdoor

3. What is the best decision for Joe to make given the ENSO phase is El Niño?

4. What is the best decision for Joe to make given the ENSO phase is La Niña?

5. What is the best decision for Joe to make given the ENSO phase is El Niño?

6. Why is the expected value for playing in the indoor league the same for each ENSO phase?

7. Why is the expected value for playing in the outdoor league the different for each ENSO phase?

Blank Decision Trees

Goal__________________________ Goal__________________________

Goal_________________________ Goal_________________________

Decision Tree Problems

For the following decision problems fill in the decision trees, provide the decision to be made, the random event and probability associated with the event, and the payoffs.

1. You must decide to bring your raincoat to the football game or leave the raincoat at home. If you bring your coat and it rains you will be happy and dry. If it does not rain, you will be dry, but you will have the hassle of carrying the coat and not using it. Finally, if you do not bring the coat and it rains you will be unhappy and wet. The weather forecast is for a 50% chance of rain.

2. The forecast is for a 10% chance of hail this evening. Your parent’s decision is to either clean up the garage to be able to park the car in the garage, or to not clean up the garage and park outside. If it hails and the car is parked in the garage, the car is OK, but you had the hassle of cleaning up the garage. If the car is parked in the garage and it does not hail, the car is still OK but you did have the hassle of cleaning the garage. If you park outside (no hassle to clean the garage) and it hails, the car is dented. If the car is parked outside and it does not hail the car is OK and you did not have to clean the garage.

3. Your teacher has stated there is a 20% chance of a test tomorrow and an 80% chance of not having a test. Develop a decision tree associated with the decision to either study after school or play. If you study and there is a test, you will have a passing grade. If you do not study and there is a test, you will fail the test. If there is no test, there is no grade that day in the class. This example illustrates that the decision does not have to be weather related.

4 There are two different roads (Baxter and River Roads) your parents can use to take you to school. In taking Baxter Road, you have to cross a railroad crossing. If there is no train (25% chance) you will make it to school on time. If there is a train (75% chance), you will be 10 minutes late to school. River Road uses an overpass to cross the railroad. If you take River Road there is no chance of being stopped by a train, but you will be one minute late for school. This example differs because it is not weather related and the decision tree has only flow out of river road because there is no train crossing.

5. NASA is faced with the decision of landing the space shuttle either in California or in Florida. Weather forecasts for both the Florida and the California landing sites are available. There is a 30% chance of storms in Florida and a 10% chance of storms in California. If there are storms at the landing site used, the shuttle will be damaged. If there is not a storm, the shuttle lands without damage. NASA also incurs an additional expense of transporting the shuttle to Florida, if the shuttle lands in California. Create a decision tree for this problem; note the chances for no storms are 100% minus the chance of storms. Hint: your decision tree should include additional costs if the shuttle lands in California.

6. This Saturday morning, you can either referee soccer or help your mom clean the house. You must sign up as a soccer referee by Thursday. If you referee and it does not rain, you will earn $65. However, if it rains, the soccer games will be cancelled and you will earn $0. You mom will pay you $20 to help clean the house. Because you are cleaning inside, you will earn this $20 regardless of the weather. The weatherman has forecasted a 20% chance of rain. Create a decision tree for this problem; note the chances for no rain are 100% minus the chance of rain.

7. You are the owner of the Good Goof Manufacturing Company. Your company uses a machine to make Good Goofs. The decision you are facing is whether to service the machine or don’t service the machine. If you service the machine, there is a 1% chance of the machine breaking down, therefore, a 99% chance of no breakdown. The cost of servicing the machine is $50. If you do not service the machine, you have service costs, but the probability of the machine breaking down increases to 3%. If the machine breaks down, it will cost $2000 to fix. Develop the decision tree for this problem

8. Decision trees are often more complex than the examples given in questions 1-7. As an example, consider Antique Dealer Inc. Antique Dealer has a client that will buy an antique tractor for $5,000. Antique Dealer Inc. has found the tractor and can either buy the tractor today for $3,000 or wait until tomorrow to buy the tractor. Tomorrow’s price is $2,500. By waiting, Antique Dealer Inc. runs the risk that someone else will buy the tractor. There is a 30% chance someone other than Antique Dealer will buy the tractor today and a 70% chance the tractor will not be sold today. Develop a decision tree for Antique Dealer’s decisions over the next two days. Antique Dealer Inc. wants to make as much money as possible. Money made by Antique Dealer Inc. is the cost of the tractor minus what they must pay for the tractor. Hint: the key to drawing this decision tree is for day one, Antique Dealer must choose between buying the tractor and waiting until day two.

-----------------------

Student Packet

5

Outdoor League

Outdoor League

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download