Question

At graduation, students have traditionally been handed their diploma on stage and then they can shake the hand of the President as they are getting their picture taken. Georgia Tech is considering ending that process due to the time it takes up combined with the typical hot weather in May. You have been asked to investigate the actual time involved and whom that affects. You are given that the students arrive on the podium based on a Poisson process at a rate of 44 per hour. The Presidents handshake and the picture typically take 1 minute per student. Based on this information, and your understanding of Queuing Theory and Probability, answer the following questions… (e) What is the probability that the President has no student to greet at anytime? (f) What is the probability that the President has a student to greet at anytime? (g) Assuming that there is a 40% chance it will rain on May 5th and that there is a 50% chance the graduation will be held on May 5th, what are the odds of it raining on graduation day?

Answer 1

(e)

Arrival rate = 44 per hour

Service rate = 1 per minute = 60 per hour

Utilization = / = 44/60 = 0.7333

Probability that the President has no student to greet at anytime = 1 - = 1 - 0.7333 = 0.2667

(f)

Probability that the President has a student to greet at anytime = = 0.7333

(g)

Probability of raining on graduation day = Probability of raining on May 5th * Probability that graduation will be held on May 5th = 0.4 * 0.5 = 0.2

Odds of it raining on graduation day = p / (1 - p) = 0.2 / (1 - 0.2) = 1/4 = 0.25