   # The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. a. Sketch this exponential probability distribution. b. what is the probability that the arrival time between vehicles is 12 seconds or less? c. What is the probability that the arrival time between vehicles is 6 seconds or less? d. What is the probability of 30 or more seconds between vehicle arrivals? 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 6.4, Problem 35E
Textbook Problem
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## The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. a. Sketch this exponential probability distribution. b. what is the probability that the arrival time between vehicles is 12 seconds or less? c. What is the probability that the arrival time between vehicles is 6 seconds or less? d. What is the probability of 30 or more seconds between vehicle arrivals?

a.

To determine

Draw the exponential probability distribution.

### Explanation of Solution

Calculation:

The time between arrivals of the vehicles in a particular intersection follows an exponential distribution with mean 12 seconds.

The exponential probability density function is,

f(x)=1μex/μ for x0

The exponential probability density function for time between arrivals is,

f(x)=1

b.

To determine

Find the probability that arrival time is less than or equal to 12 seconds.

c.

To determine

Find the probability that arrival time is less than or equal to 6 seconds.

d.

To determine

Find the probability that arrival time is greater than or equal to 30 seconds.

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