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Twelve Customers Arrive at the Lunch Counter at George's Happy

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Twelve customers arrive at the lunch counter at George's Happy Hog per hour and select the hickory smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take and fill an order in three minutes on average. What is the lowest number n such that the likelihood of n or more customers in line and receiving service is 0? Assume that the arrival and service times can be assumed as exponentially distributed.

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Definitions:

Monozygotic

Referring to twins that originate from a single fertilized egg, resulting in individuals that are genetically identical.

Zygotes

The initial cell formed when a sperm cell and an egg cell merge, representing the first stage of development in many multicellular organisms.

Longitudinal Design

Research design in which one participant or group of participants is studied over a long period of time.

Cohort

A group of people banded together or treated as a group, often used to define individuals born around the same time who experience similar cultural or historical events.

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