Exercise 19 Page 968

We are given the results of a survey about the sale of books in each quarter. Let's design a simulation to estimate the probability that a random book will be sold in each quarter. First let's review the steps for designing a simulation.

1. State each possible outcome and the corresponding theoretical probability.
2. Determine if there are any assumptions.
3. Choose and describe an appropriate probability model for the situation.
4. 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 book will be sold in each of the $4$ quarters of a year, we have $4$ possible outcomes. Based on the given information, we will assume that the theoretical probability that a book will be sold in a particular quarter is equal to the given percentages.

Step $2$

We will also assume that the trends in selling the books 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.

Now we are ready to create our spinner. Each trial — one spin of the spinner — will represent the quarter in which a random book is sold.

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.