Chapter 13, Problem 20SGR

To determine

Describe how you would use the geometric probability model to design a stimulation.

Explanation of Solution

Given:

The US consumes 17.3 million barrels of oil a day. 63% is used for transportation , 4.9% is used to generate electricity, 7.8% is used for heating and cooking, and 24.3% is used for industrial processes.

Calculation:

Step 1 :

Possible Outcomes	Theoritical Probability
Transportation	63%
Generate electricity	4.9%
Heating and cooking	7.8%
Industrial processes	24.3%

Step 2:

The simulation will consist of 100 trials.

Step 3:

We can use a spinner divided into four sectors :

one containing 63% of spinner’s area , second containing 4.9% of spinner’s area , third containing 7.8% of spinner’s area , and the fourth containing 24.3% of spinner’s area .Find the measurement of central angle of each sector.

Transportation = $63\%\text{ of }360°=226.8°$ : Blue sector

Generate electricity = $4.9\%\text{ of 360}°\text{ = 17}\text{.64}°$ : Yellow sector

Heating and cooking = $7.8\%\text{ of 360}°\text{ = 28}\text{.08}°$ :Sky Blue sector

Industrial processes = $24.3\%\text{ of 360}°\text{ = 87}\text{.48}°$

: Red sector

Step 4:

A trial means one spin on the spinner , represents the use of electricity in which sector .

The simulation will consist of 100 trials.

Perform 100 trials and record the result.