It's a Beautiful Sunny Day After a Week of Rainy

question 33

Essay

It's a beautiful sunny day after a week of rainy weather and both of the local car washes are busy. One car wash is fully automated, touchless, and can wash a vehicle of any size to a dazzling luster in 5 minutes flat. The other car wash is a fund raiser staffed by eager amateurs that work on one car at a time and can finish it in about 4 minutes (their time is governed by the Poisson distribution). Customer arrivals at both car washes are Poisson distributed with a mean of 10 per hour. How long does it take the average customer to work his way through either system? How many customers are in the systems on average?

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Definitions:

Sodium Channels

Specialized protein molecules in cell membranes that allow the passage of sodium ions into and out of the cell, playing a crucial role in generating and conducting electrical signals.

Graded Potentials

Changes in electrical charge across the cell membrane that vary in size and are not propagated in an all-or-none manner.

Channels

Structures or means through which substances or signals are able to pass or be conveyed in a biological system.

Channels

Pathways or conduits through which substances such as ions or molecules can move across cell membranes or within the body or an organism.