A relay race is run between team A and team B. Each team has four runners, who successively run around a track and pass a baton to the next runner in their team when they have finished. The team finishes when the fourth runner has completed the run. The runners on team A take times with an expectation of 33.2 seconds and a standard deviation of 1.4 seconds, while the runners on team B take times with an expectation of 33.0 seconds and a standard deviation of 1.3 seconds. The times of all eight runners are independent of each other.
(a) What are the expectation and the standard deviation of the total time taken by team A?
(b) An official measures the total time taken by team A and subtracts from it the total time taken by team B? What are the expectation and the standard deviation of this difference?
(c) The manager of team A measures the time taken by the fust runnei- on team A and subtracts from it the average of the times of the other three runners on team A. What are the expectation and the standard deviation of this difference?