Nathan is cutting it close today. At 10:00:00 AM, the professor will close the door to the classroom and ignore any requests to enter the room once his scintillating lecture has begun
The soda machine outside the lecture hall sees a steady stream of customers throughout the day. While the machine takes 4 seconds to deliver a can of carbonated sugar water once the button is pressed, the student customers introduce variation into the delivery process by pondering their selection for a while. Thus, we can safely say that the service time is governed by a negative exponential probability distribution that averages 10 seconds. Over the course of a twelve hour lecture day, students arrive at the rate of 240 per hour, Poisson distributed of course.
Nathan approaches the soda machine at 9:59:20. Will he make it to class on time?
A) Nathan will be late by ten seconds.
B) Nathan will be exactly on time.
C) Nathan will be early by ten seconds.
D) Nathan will be early by twenty seconds.
Answer: C
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