We are given that the United States consumes 17.3 million barrels of oil a day and we have a list of 4 sectors that use oil. Let's design a simulation to estimate the probability that a random barrel of oil will be used in each sector. First let's review the steps for designing a simulation.
Choose and describe an appropriate probability model for the situation.
Define a trial for the situation and choose the number of trials to be conducted.
Let's follow these steps, one at a time.
Step 1
Since we are interested in the probability that a random barrel of oil will be used in each of the 4 sectors, we have 4 possible outcomes. Based on the given information, we will assume that the theoretical probability that a barrel of oil will be used in a particular sector is equal to the given percentages.
Possible Outcomes
Theoretical Probability
Transportation
63 %
Electricity
4.9 %
Heating and Cooking
7.8 %
Industrial Processes
24.3 %
Step 2
We will also assume that the trends in using the barrels of oil stay approximately constant during the time period.
Step 3
Since we are asked to use a geometric probability model, we can use a spinner divided into 4 sectors — each sector representing one of the probabilities. Let's calculate the measure of the central angle of each sector.
Possible Outcomes
Measure of the Central Angle
Transportation
63 %* 360^(∘)=226.8^(∘)
Electricity
4.9 %*360^(∘)≈ 17.6^(∘)
Heating and Cooking
7.8 %*360^(∘)≈ 28.1^(∘)
Industrial Processes
24.3 %*360^(∘)≈ 87.5^(∘)
Now we are ready to create our spinner. Each trial — one spin of the spinner — will represent the sector in which a random barrel of oil is used.
Step 4
Finally, let's choose the number of trials to be 50. The results of conducting the described simulation can be recorded in a frequency table and used to evaluate the experimental probabilities. Keep in mind that this is just one possible simulation we can create.
