$1.$ The new shopping mall is considering setting up an information desk manned by one employee. The layout for this mall is quite complex, leading the mall manager to expect higher than normal arrival rate for persons seeking assistance. It appears that a reasonable expectation is an arrival rate of approximately $25$ patrons per hour. Under the original plan, the manager expected that it would take approximately four minutes for the Information Desk employee to help the average person. By utilizing a new map and special guide signs, the manager believes that the required service time can be reduced to an average of two minutes per person. If he implements the new map and guide signs:

$($a$)$ What the probability that the Information Desk employee is idle?

$($b$)$ What is the proportion of the time that the Information Desk employee is busy?

$($c$)$ What is the average number of people receiving and waiting to receive some information?

$($d$)$ What is the average number of people waiting in line to get some information?

$($e$)$ What is the average time a person seeking information spends waiting and being served by the Information Desk employee?

$($f$)$ What is the expected time a person spends just waiting in line to have his question answered?

$($g$)$ Do you think the manager should implement the plan or should he try to find another possible solution? $$Why$?$ or $$Why not?$.$