Chapter 13, Problem 19SGR

To determine

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

Explanation of Solution

Given:

According to a survey, people buy 30% of their books in October, November, and December , 22% during January, February, and March, 23% during April , May, and June, and 25% during July, August, and September.

Calculation:

Step 1 :

Possible Outcomes	Theoritical Probability
People buy books in October, November, and December	30%
People buy books in January, February, and March	22%
People buy books in April , May, and June	23%
People buy books in July, August, and September	25%

Step 2:

The simulation will consist of 100 trials.

Step 3:

We can use a spinner divided into four sectors :

one containing 30% of spinner’s area , second containing 22% of spinner’s area , third containing 23% of spinner’s area , and the fourth containing 25% of spinner’s area .Find the measurement of central angle of each sector.

People buy books in October, November, and December = $30\%\text{ of }360°=108°$ : Blue sector

People buy books in January, February, and March = $22\%\text{ of 360}°\text{ = 79}\text{.2}°$ : Yellow sector

People buy books in April , May, and June = $23\%\text{ of 360}°\text{ = 82}\text{.8}°$ :Sky Blue sector

People buy books in July, August, and September = $25\%\text{ of 360}°\text{ = 90}°$

: Red sector

Step 4:

A trial means one spin on the spinner , represents the month in which books are bought .

The simulation will consist of 100 trials.

Perform 100 trials and record the result.