Question

Question 3.
It takes an average of 55 minutes to fly from YYZ to New York’s JFK airport, averaged across all airlines. The variance of all flights is 49 minutes. Sixty percent of passengers tend to be male.

3a. A new airline is hoping to reduce this flight time. They will use the same variance and standard deviation as its measure of variability. Explain why this is a statistically valid method.

3b. It takes an average of 58 minutes to fly to New York’s LGA, across all airlines. Is there a difference between flight times to the two New York airports?

3c. After eight flights, a frequent flyer calculated that on average it took 49 minutes (with a standard deviation of 5.5 minutes) to get from YYZ to JFK. He claims that the airline likes him, so they fly faster when he is on board. Is his claim supported? What is another explanation?

3d. Down-winds occur when air moves in the same direction as the plane. To test whether this reduces flight times, an airline took 10 cases where the flights flew down-wind and 5 cases where the plane flew up-wind (where the air is moving in the opposite direction of the destination). For down-wind flights it took on average 49 minutes (s = 5.32), and for up-wind flights it took an average of 61 minutes (s = 4.47). Do these flights differ from the average time?

3e. Related to 3d, both down-wind and up-wind airflow caused a change of 6 minutes flight time. Explain why, even though the absolute change is the same, the statistical results differed.

3f. What is the probability of boarding a flight from YYZ to JFK and it taking 47 minutes or less?

3g. Because YYZ-JFK is such a short flight, small regional jets usually operate this route. Commonly, airlines use the CRJ700 series aircraft, with capacity for 70 passengers. One flight had less than 40 males and took less than 50 minutes. What is the probability of this occurrence?

3h. What is the probability of a flight taking between 46 and 56 minutes or between 53 and 61 minutes, and having between 39 and 52 males but not 45 males? This flight is on the CRJ700 series aircraft with 70 seats.

3i. Theoretically, is it safe to assume gender and flight time are independent? Explain.

3j. On that same 70-seat CRJ700, what is the probability that a flight will take longer than 58 minutes and have less than 39 males, or be faster than 49 minutes and have more than 40 males?

Answer 1