During registration at Accra Institute of Technology (AIT) for every semester, students in the Engineering Department of the Sea View campus must have their courses approved by one course advisor, Dr. Haruna. It takes the advisor an average of 2 minutes to approve a course, and students arrive at the advisor’s office at the rate of 28 per hour. 

a) i. Examine the average time (in minutes) a student waits in the queue to be served?

ii. Assess the probability that at any point in time 10 students are in the registration process? 

b) i. Estimate the average number of students waiting, correct to the nearest whole number?

ii. The University (AIT) policy is to have the course advisor working 60% of the time in order to have time for other teaching services. What must the arrival rate be for Dr. Haruna to be as busy as management would like? 

c) The Dean of the school has received a number of complaints from students about the length of time they must wait to have their courses approved. The Dean has two options available to solve this. He can either hire a Teaching Assistant (TA) to help Dr. Haruna to serve the 3 students, or assign the task to the Department Secretary. The TA can serve 40 students each hour but must be paid GH₵ 300 for this job. The Secretary can serve a student every minute and need not be paid any extra amount for this task. However, this will delay the other duties of the Secretary, which is estimated to cost GH₵ 500. Which option should the Dean go for if the school stands to save GH₵ 50 for each minutes saved?