When a shipment of packages arrives at a warehouse, an automated sorting system sorts the packages based on their destination. Sorting the packages efficiently ensures that they can be loaded onto the appropriate delivery trucks on time. It is crucial that the sorting process is completed before the trucks leave the warehouse.

$($a$)(3$ marks$)$ The time taken to load the packages onto the trucks is $5\mathrm{.}8$ hours. Sorting System $($Type A$)$ sorts one half of the shipment first and then the other half. The sorting time for each half is Normally distributed with a mean of $2\mathrm{.}5$ hours and a standard deviation of $0\mathrm{.}5$ hours. The sorting times for the two halves are correlated with a correlation coefficient of $0\mathrm{.}6.$ What is the probability that the sorting system will finish sorting the entire shipment before the trucks are fully loaded?