Introduction

Take a look at this report produced by the Aviation Consumer Protection Division of the Office of Aviation Enforcement and Proceedings, which is a part of the US Department of Transportation. Specifically, you're interested in table 2, on-time flight arrivals, which starts on page 6 and ends on page 9. The data in the table is from a typical month, so each percentage in the table can be thought of as a probability. You can answer many probability questions using this table.

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Directions and Analysis

Task 1: Questions You Can Answer with Table 2

Refer to table 2 of the Air Travel Consumer Report to answer these questions.

1. Given that a randomly chosen flight arrives in Atlanta (ATL), what is the probability that it arrives on time?

Type your response here:

1. Given that a randomly chosen US Airways (US) flight arrives in Denver (DEN), what is the probability that it arrives on time?

Type your response here:

1. Given that a randomly chosen flight arrives in Los Angeles (LAX), what is the probability that the carrier is American Airlines (AA)?

Type your response here:

1. Chicago has two airports (MDW and ORD). If you're flying with Delta Airlines (DL) and your primary concern is to arrive on time, is it better to fly to MDW or to ORD?

Type your response here:

1. New York City has two airports (JFK and LGA). If you're flying with United Airlines (UA) and your primary concern is to arrive on time, is it better to fly to JFK or to LGA?

Type your response here:

Task 2: Questions That Are Difficult or Nearly Impossible to Answer with Table 2

Many questions are difficult or nearly impossible to answer using table 2 in its current form. Since computing the answers to these questions is difficult or close to impossible, just give the formulas you would need to obtain the answers to these questions.

1. What is the probability that a randomly chosen flight arrives on time?

Type your response here:

1. Overall, which carrier has the highest probability of arriving on time?

Type your response here:

1. Given that a randomly chosen flight arrives on time, what is the probability that it arrives in Philadelphia (PHL)?

Type your response here:

1. Given that the carrier is Hawaiian Airlines (HA), what is the probability that a randomly chosen flight arrives on time?

Type your response here:

1. If you're a frequent flyer who travels to many different airports, and you have the choice between SkyWest Airlines (OO) and Southwest Airlines (WN) for all your flights, which carrier should you choose if your primary concern is arriving on time?

Type your response here:

Task 3: Transforming Table 2

The reason it was difficult or nearly impossible to answer the questions in task 2 is that table 2 isn't quite a two-way table. In other words, there is a total row at the bottom of the table, but there is no total column at the right of the table. In this activity, you'll transform the table into a proper two-way table.

Open this spreadsheet. The worksheet labeled Original contains the data as it appears in the report. Scroll through the data in this worksheet and do a spot check to verify that it is, in fact, the same table. This will give you some practice in navigating the table.

Once you are comfortable navigating, click the Modified tab. In this worksheet, a few changes have been made to the table:

• Cells that contained H/ in the original table now contain zeros. H/ indicated that a particular carrier didn't have a hub at a particular airport. In other words, it had 0 arriving flights with 0% arriving on time.
• For each airport, an additional column labeled # ON TIME has been added.
• On the far right, you will find a TOTAL area with three new columns: # OF ARR., # ON TIME, and % ON TIME.

By filling in all of the blank columns, you'll transform the table into a two-way table. Below you'll find instructions for filling in the blank columns to complete the two-way table.

Before you start, make a copy of the Modified worksheet in case you make a mistake. One way to do this is to right-click the Modified tab, select Move or Copy on the shortcut menu, select the Create a copy checkbox, and click OK. This procedure may vary slightly depending on your version of Microsoft Excel. If you make a mistake, just delete the Modified tab you created by right-clicking it and selecting Delete from the shortcut menu. Then make a new copy of the Modified worksheet and start again.

To complete the # ON TIME column for each airport:

• Click in cells C8-C22 and look at the formula bar to get an understanding of the formulas in these cells. Do the same with cell C23.
• Copy cells C8-C23, and paste them into the space for cells F8-F23.
• Verify that all the formulas are doing what you expect.
• Repeat this procedure to fill in the # ON TIME column for each individual airport.

To complete the TOTAL area on the right:

• Go to columns CK and CL at the far right of the table. Examine what the formulas do for rows 8-22. Now examine the formula in cells CK23 and CL23.
• Click in Cell CM8.
• Enter a formula in the formula bar that will calculate what percentage of total arrivals are on-time arrivals.
• Once you're satisfied this formula works, copy it into all the cells in that column (CM8-CM22, plus CM23).

Task 4: Questions That Can Now Be Answered by Table 2

Remember those questions that were difficult or nearly impossible to answer with table 2? See if you can answer them now, using the spreadsheet you modified.

1. What is the probability that a randomly chosen flight arrives on time?

Type your response here:

1. Overall, which carrier has the highest probability of arriving on time?

Type your response here:

1. Given that a randomly chosen flight arrives on time, what is the probability that it arrives in Philadelphia (PHL)?

Type your response here:

1. Given that the carrier is Hawaiian Airlines (HA), what is the probability that a randomly chosen flight arrives on time?

Type your response here:

1. If you're a frequent flyer who travels to many different airports, and you have a choice between SkyWest Airlines (OO) and Southwest Airlines (WN) for all your flights, which carrier should you choose if your primary concern is arriving on time?

Type your response here:

Task 5: Applying Conditional Probability to a Real-World Scenario

Gary Foshee created a popular probability puzzle that goes like this: "I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"

In this puzzle, knowing that one of Gary's children was born on a Tuesday is as important as knowing that he has one boy. Assuming that having boys and girls are equally likely and that births are equally likely on every day of the week, what is the probability that Gary has two boys, given the available information? (Hint: When Gary said that one is a boy born on a Tuesday, he meant at least one child is a boy born on a Tuesday.)

Type your response here: