### Aviation Applications Problem Set II MAT 211

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AVIATION APPLICATIONS PROBLEM SET II

This is the second of three aviation applications problem sets that you will complete for Math 211. It is worth 100 points or 10% of your course grade.

To complete the assignment, first save this Word document on your computer or memory device. Then complete each of the problems or questions by answering the problem or question in the Word document you saved.

Where appropriate, you must show your work and you must clearly indicate your answer. In some cases, showing your work can be done by pasting appropriate Excel or PHStat output into the Word file. Dont just paste the Excel or PHStat output into the documentalso clearly indicate your answer.

When you complete the assignment, save it, and then turn it in using the Blackboard Assignment Tool. If you have questions, please ask your instructor.

You will need the following Excel data files to complete this problem set:

AAL Pax 07

ATL Taxi Times

According to U.S. Department of Transportation Data, in April of 2008, there were 253,190 complaints related to mishandling of baggage by U.S. Airlines. Mishandling includes lost, damaged, delayed, or pilfered baggage. The same data set also shows a total of 50,755,213 enplaned passengers during April 2008.

Assuming that the April 2008 numbers are typical for U.S. Airlines, what is the probability that a randomly selected passenger would have his or her luggage mishandled by airlines? Round your answer to three significant digits.

Lost luggage seems to be a favorite topic of travel experts and sometimes late-night talk show comedians. Travel expert Peter Greenberg is quoted as saying, There are two types of bags: Carry-on and lost. Greenberg suggests sending your luggage ahead of you using FedEx or luggage services. Based on your answer to part a, is it unusual for a passenger to have mishandled luggage? Is Peter Greenbergs comment and advice warranted? Explain your answers.

The answer from part a corresponds to luggage being lost about 0.5% of the time. This is high enough to warrant the advice in my opinion. This percentage means that 1 out of every 200 passengers will lose luggage.

In computing the probability of a randomly selected passenger having his or her luggage mishandled, we used the total number of enplaned passengers. Do you think that is the correct number to use? Explain your answer.

The following table gives the taxi times for Continental Airlines Flight 1421 from Cleveland to Denver during the month of April 2008. (Note: You can copy and paste the table into Excel if necessary.)

Complete the third column of the table by computing the probability of each taxi time. Round your answers to two decimal places.

Taxi Time# FlightsProbability

American Airlines Flight 179 from New York to San Francisco uses a Boeing 767-300 with 213 seats. Because some people with reservations dont show up, American Airlines can overbook by accepting more than 213 reservations. If the flight is not overbooked, the airline will lose revenue due to empty seats, but if too many seats are sold and some passengers are denied seats, the airline loses money from the compensation that must be given to the bumped passengers. Assume that there is a 0.0995 probability that a passenger with a reservation will not show up for the flight (based on data from the IBM research paper Passenger-Based Predictive Modeling of Airline No-Show Rates by Lawrence, Hong, and Cherrier). Also assume that the airline accepts 236 reservations for the 213 seats that are available.

Find the probability that when 236 reservations are accepted for Flight 179, there are more passengers showing up than there are seats available. That is, find the probability of more than 213 people showing up with reservations, assuming that 236 reservations were accepted. Round your answer to three decimal places.

Find the maximum number of reservations that could be accepted so that the probability of having more passengers than seats is 0.05 or less. (Hint: You can use PHStat and a trial-and-error approach to determine the answer.)

Under older Federal Aviation Administration rules, airlines had to estimate the weight of a passenger as 185 pounds. (That amount is for an adult traveling in winter, and it includes 20 pounds of carry-on baggage.) Current rules require an estimate of 195 pounds. Based on data from the National Health and Nutrition Examination Survey, men have weights that are normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds.

If a Boeing 767-300 is full of 213 adult male passengers and each is assumed to have 20 pounds of carry-on baggage, find the probability that the mean passenger weight is greater than 195. Does the pilot have to be concerned about exceeding this weight limit?

In problem 8 of Problem Set I, we assumed that the number of passengers carried per month by Alaska Airlines out of the Anchorage Airport was normally distributed and then we did some calculations based on that assumption. The number of passengers per month is in Data File AAL Pax 07.

Construct a normal probability plot and determine whether the assumption of normality appears to be valid. Explain your answer.

Compute the mean and median for the data set. Does comparison of the mean and median support the conclusion you made in part a? Explain your answer.

- A 2005 Bureau of Transportation Statistics study reported that of 273 airline passengers surveyed, 246 reported that they were satisfied or very satisfied with the overall experience at the passenger security check point.

Construct a 95% confidence interval estimate of the proportion of passengers satisfied or very satisfied with the overall experience at the passenger security checkpoint. What is the margin of error? Round your answers to three decimal places.

Construct a 99% confidence interval estimate of the proportion of passengers satisfied or very satisfied with the overall experience at the passenger security checkpoint. What is the margin of error? Round your answers to three decimal places.

Which confidence interval is wider? Explain why?

The 99% confidence interval is wider because with the increase in the percentage of confidence, the confidence

Explain the meaning of the 95% confidence interval.

- A 2005 Bureau of Transportation Statistics study reported that 90.1 % of airline passengers surveyed reported that they were satisfied or very satisfied with the overall experience at the passenger security check point.

Assuming that the 90.1% figure is correct, how large a sample would be required to reduce the margin of error for a 95% confidence interval estimate of the proportion of passengers satisfied or very satisfied with the overall experience at the passenger security checkpoint to .03?

Assuming that the 90.1% figure is correct, how large a sample would be required to reduce the margin of error for a 95% confidence interval estimate of the proportion of passengers satisfied or very satisfied with the overall experience at the passenger security checkpoint to .02?

For a fixed level of confidence, what is the relationship between sample size and margin of error?

- With rising fuel costs, the amount of time it takes for an airliner to taxi from the departure gate to takeoff is a concern. Data File ATL Taxi Times gives taxi times for random samples of 100 flights in July 2000 and in July 2007 at the Atlanta Hartsfield Airport.

Construct a 95% confidence interval estimate of the mean taxi time at the Atlanta airport in July 2000.

Construct a 95% confidence interval estimate of the mean taxi time at the Atlanta airport in July 2007.

Based on your answers to parts a and b, can you conclude that taxi times increased between 2000 and 2007 at the Atlanta Airport?

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