Two high-speed automated packaging lines, Line A and Line B, are used to process identical orders. The time taken by Line A to process an order, in seconds, is normally distributed with mean 12.5 and variance 0.36. The time taken by Line B to process an order, in seconds, is normally distributed with mean 13.2 and variance 0.64. Processing times for all orders and lines are independent.
Determine the probability that, for a single randomly selected order, Line B completes the packaging faster than Line A.
A factory uses these lines to process a batch of 150 orders on Line A and a separate batch of 150 orders on Line B. Both lines start simultaneously.
Calculate the probability that the total time taken by Line B to complete its batch exceeds the total time taken by Line A by more than 120 seconds.
