Suppose three mutually independent factors cause baggage delays: (1) mechanical issues, (2) employee error, or (3) computer
Question:
Suppose three mutually independent factors cause baggage delays: (1) mechanical issues, (2) employee error, or (3) computer system issues. Each factor has a normal distribution with mean 0 and standard deviation of 3, where delays are measured in minutes. Each of these variables is continuous and can take negative values. On January 31, flight 9371 had a total baggage delay of 10 minutes, with 〖 X〗_1=8 (mechanical), X_2=1 (employee), and X_3=1 (computer system). Your manager asks you to find out how unusual it is among baggage delays of exactly 10 minutes that the mechanical delay is 8 minutes or more. That is, given that the total delay is 10 minutes, what is the probability that the mechanical delay is ≥ 8 minutes?
Probability and Statistics
ISBN: 978-0321500465
4th edition
Authors: Morris H. DeGroot, Mark J. Schervish