Question 2 (6 parts): The turnaround of a passenger flight on a small aircraft (from arrival to departure) depends on processes involving both the passenger cabin and the baggage hold. Focusing only on the passenger cabin, three processes must take place in sequence: Process Mean () Standard Deviation (a) Deboarding 12 minutes 3 minutes Cabin Cleaning 6 minutes 2 minutes Boarding 14 minutes 4 minutes Assume that the time it takes to complete each task is Normally-distributed with known meand and standard deviation, and that each task is independent of the others. a. What is the probability that deboarding the plane takes less than 15 minutes? b. What is the probability that boarding the plane takes less than 15 minutes? c. What is the probability that the entire process takes more than 35 minutes? Hint: the process requires deboarding, cabin cleaning, and boarding (one after the other) in sequence with no time between tasks. d. A process engineer decides to measure the turnaround time for a random sample of 20 flights. What is the probability that the entire process takes more than 35 minutes for over half of the 20 flights in this sample? Hint: the process requires deboarding, cabin cleaning, and boarding (one after the other) in sequence with no time between tasks. e. For the same sample of 20 flights, what is the probability that the sample mean for the entire process takes more than 35 minutes? Hint: the process requires deboarding, cabin cleaning, and boarding (one after the other) in that sequence. f. The airline believes that the boarding process can be reengineered so that the mean and standard deviation of boarding could be reduced to / = 12.5 and o = 3, respectively. Using the reengineered boarding process instead of the original boarding process, what is the new probability that the entire process takes more than 35 minutes? Hint: the process requires deboarding, cabin cleaning, and boarding (one after the other) in sequence with no time between tasks