Waiting for a car wash. An automatic car wash takes

Chapter 4, Problem 82E

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QUESTION:

Problem 82E

Waiting for a car wash. An automatic car wash takes exactly 5 minutes to wash a car. On average, 10 cars per hour arrive at the car wash. Suppose that 30 minutes before closing time, 5 cars are in line. If the car wash is in continuous use until closing time, is it likely anyone will be in line at closing time?

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QUESTION:

Problem 82E

Waiting for a car wash. An automatic car wash takes exactly 5 minutes to wash a car. On average, 10 cars per hour arrive at the car wash. Suppose that 30 minutes before closing time, 5 cars are in line. If the car wash is in continuous use until closing time, is it likely anyone will be in line at closing time?

ANSWER:

Solution :

Step 1 of 1:

Let the number of cars that arrive at the car wash at 30 minute.

We know that on an average 10 cars per hour arrive at the car wash.

Let X follows a Poisson distribution with mean = 5.

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