Final answer:
In this scenario, there are 4 routes between a person's home and work, with two one-way routes. A tree diagram is used to visualize the various ways the person can go to and from work. By counting the routes, we can determine the percent of commuters traveling alone to work and calculate the number of workers traveling alone and driving in a carpool if 1,000 workers are selected randomly.
Step-by-step explanation:
The Tree Diagram
a. Finding the Percent of Commuters Traveling Alone
To find the percent of commuters traveling alone to work, we need to count the number of routes they can take. From the tree diagram, we can see that there are 2 routes available for the way to work (A or D) and 3 routes available for the way home (A, D, or B). The total number of possible routes is the product of these two numbers, which is 2 * 3 = 6. Since only one route is for traveling alone (A), the percent of commuters traveling alone is 1/6 = 16.67%.
b. Number of Workers Traveling Alone
If 1,000 workers are randomly selected, we can expect that approximately 16.67% of them would travel alone to work. To find the number of workers, we multiply the percent by the total number of workers: 0.1667 * 1000 = 166.7 workers. Since we cannot have a fraction of a worker, we can round it to the nearest whole number. So, approximately 167 workers would travel alone to work.
d. Number of Workers Driving in a Carpool
From the tree diagram, we can see that only 1 route (B) is for driving in a carpool. So the percent of workers driving in a carpool is 1/6 = 16.67%. Applying the same calculation as in Part b, we can expect that approximately 16.67% of the 1,000 workers would drive in a carpool. So, approximately 167 workers would drive in a carpool.