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13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

Chapter 5, Problem 69SE

Textbook Problem

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Cars arrive at a car wash randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 15 cars per hour. What is the probability that 20 or more cars will arrive during any given hour of operation?

To determine

Compute the probability that 20 or more cars will arrive during any given hour of operation.

**Calculation:**

In a car wash, cars arrive independently. The probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 15 cars per hour.

Define the random variable *x* as the number cars that will arrive during any given hour of operation. Here, the occurrence of cars is random and the cars arrive independently at the car wash. The mean number of arrival rate is 15 cars per hour. That is, the occurrences (cars) are uniformly distributed for every hour. Thus, the number of cars that will arrive during any given hour of operation has Poisson distribution with parameter,

The Poisson probability function is,

Where, *x* is the number occurrences of the event in a given interval, *e* is a constant that has value 2.71828.

The required probability is obtained by substituting the values *x* values in the Poisson probability function till the probability becomes zero. The probability that 20 or more cars will arrive during any given hour of operation is obtained as shown below:

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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