Approximately 86.5% of Americans commute to work by car,...

Approximately 86.5% of Americans commute to work by car, truck, or van. Out of that group, 84.6% drive alone and 15.4% drive in a carpool. Approximately 3.9% walk to work and approximately 5.3% take public transportation. a. Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work. b. Assuming that the walkers walk alone, what percent of all commuters travel alone to work? c. Suppose that 1,000 workers are randomly selected. How many would you expect to travel alone to work? d. Suppose that 1,000 workers are randomly selected. How many would you expect to drive in a carpool?

Approximately 86.5% of Americans commute to work by car, truck, or van. Out of that group, 84.6% drive alone and 15.4% drive in a carpool. Approximately 3.9% walk to work and approximately 5.3% take public transportation.
a. Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.
b. Assuming that the walkers walk alone, what percent of all commuters travel alone to work?
c. Suppose that 1,000 workers are randomly selected. How many would you expect to travel alone to work?
d. Suppose that 1,000 workers are randomly selected. How many would you expect to drive in a carpool?

Key Concepts

Percentages

Percentages represent parts per hundred and are a common way to express proportions in statistics. They provide a straightforward method to understand and compare the share of different categories within a whole, such as the different modes of commuting. This concept is essential for converting raw data into easy-to-understand fractions and for performing calculations related to groups and subgroups.

Tree Diagram

A tree diagram is a visual tool used to systematically represent all the possible outcomes or categories of a process, especially when these outcomes have multiple levels. It is particularly useful in breaking down data into subcategories, such as different commuting methods and their further subdivisions, enabling clearer visualization of relationships between categories.

Conditional Probability

Conditional probability deals with the likelihood of an event occurring given that another event has already occurred. In the context of commuting methods, it is applied when calculating the percentages of people who drive alone or carpool from among those who drive, thus layering the percentages and showing how the likelihood of one event depends on another.

Expected Value

The expected value is a fundamental concept in probability and statistics that represents the anticipated average result when an experiment or process is repeated many times. For example, when sampling 1,000 workers, the expected value helps predict the number of individuals who travel alone or carpool based on provided percentages.

Data Representation

Data representation involves organizing and displaying information in formats such as tables and diagrams, which facilitate quick understanding and analysis. Using structured formats like tables or tree diagrams helps in breaking down complex statistical data into manageable parts, making it easier to interpret the proportions and relationships between different groups.

Transcript

00:01 125, approximately 86 .5 % of americans commute to work by car truck or van.

00:05 Out of that group, 84 .6 % drive alone and 15 .4 % drive in a carpool.

00:12 Approximately 3 .9 % walk to work, approximately 5 .3 take public transportation.

00:17 Part a.

00:18 Construct a table or tree diagram of the situation, include a branch for all other modes of transportation to work.

00:25 So they mentioned three different ways to get to work.

00:29 So we have transportation by car, truck, or van.

00:33 We have walking, which is 3 .9%, and we have public transportation.

00:39 Because in a tree diagram, this should total 100%.

00:42 We're going to say that our fourth is other, and that's going to be the remaining 4 .3 % of people.

00:50 So the problem also tells us that out of the people who travel by car, truck, or van, that 84 .6 drive alone and 15 .4 carpool to work.

01:01 So we're going to set up a second branch here, and we're going to say drive alone.

01:06 We'll call that a, and we'll say carpool is c.

01:10 We have 0 .846, drive alone, and 15 .4 .4, the carpool.

01:23 Because this is all the information we have at this point, our tree diagram is complete.

01:31 B, assuming that the walkers walk alone, what percent of all commuters travel alone to work? so what we can do here is assuming that our walkers walk alone, we have every bit of our walkers are walking along, so that's 0 .039...

Please give Ace some feedback