Chapter 13, Problem 21PT

To determine

Design a simulation using a geometric probability model .Report the results using appropriate numberical and graphical summaries.

Explanation of Solution

Given:

This quarter , T earned A in his classes 45% of the time.

Calculation:

Step 1 :

Possible Outcomes	Theoritical Probability
T score A	45%
T does not score A	(100-45)% = 55%

Step 2:

The simulation will consist of 50 trials.

Step 3:

We can use a spinner divided into two sectors, one containing 45% of spinner’s area and the other containing 55% of spinner’s area .Find the measurement of central angle of each sector.

T score A = $45\%\text{ of }360°=162°$ : Blue sector

T does not score A = $55\%\text{ of 360}°\text{ = 198}°$

: Yellow sector

Step 4:

A trial means one spin on the spinner , represents score of T ( gets A or does not get A) in classes.

A successful trial will be T scores A and a failed trial means not score A.

The simulation will consist of 50 trials.

Now, we record the results :

Possible Outcomes	Theoritical Probability	Frequency	Experimental Probability
T score A	45%	20	40%
T does not score A	55%	30	60%
Total		50