Final answer:
The mathematical components of the question involve the analysis of student arrival rates to a cafeteria, conversion of percentages to probabilities, and statistical evaluation of wait times.
Step-by-step explanation:
The subject matter of this question touches on several facets related to a campus cafeteria, including student behavior, cafeteria capacity, and statistical analysis. The actual mathematical question revolves around the arrival rates of students to the cafeteria and the probability calculation related to these rates. To address the student's implicit question explicitly, we need to utilize principles of statistics, probability, and possibly queuing theory. This requires an understanding of mean arrival rates and how to convert percentages into probabilities for these types of scenarios.
For example, if 5 students enter the cafeteria every minute, 10% leave upon seeing a long line. This would mean on average, 0.5 students (10% of 5) leave without joining the line every minute. Answers to questions like the average time between arrivals (two minutes in this case) or the probability of a customer waiting longer than five minutes before the next customer arrives (which can be calculated using exponential distribution) would involve such statistics and probabilities. Additionally, analyzing whether the variability in wait times is less than a specified duration, in the context of customer satisfaction in a single line setup, involves hypothesis testing.