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The time between arrivals of taxis at a busy intersection

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 121E Chapter 4.8

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 121E

Problem 121E

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.

(a) What is the probability that you wait longer than one hour for a taxi?

(b) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 10 minutes?

(c) Determine x such that the probability that you wait more than x minutes is 0.10.

(d) Determine x such that the probability that you wait less than x minutes is 0.90.

(e) Determine x such that the probability that you wait less than x minutes is 0.50.

Step-by-Step Solution:

Solution

Step 1 of 5

Let X be the time between the arrivals of taxi

Here X is exponential random variable with mean of 10 min

Then

             

a) We have to find the probability that you wait longer than one hour for taxi

Here one hour=60 minutes

The cumulative density function of exponential distribution is

We have to find

                                             =

                                             =

                                             =0.0025

Hence the probability that you wait longer than one hour for taxi is 0.0025


Step 2 of 5

Chapter 4.8, Problem 121E is Solved
Step 3 of 5

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

This full solution covers the following key subjects: Probability, minutes, wait, determine, such. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. Since the solution to 121E from 4.8 chapter was answered, more than 2462 students have viewed the full step-by-step answer. The answer to “The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.(a) What is the probability that you wait longer than one hour for a taxi?(b) Suppose that you have already been waiting for one hour for a taxi. What is the probability that one arrives within the next 10 minutes?(c) Determine x such that the probability that you wait more than x minutes is 0.10.(d) Determine x such that the probability that you wait less than x minutes is 0.90.(e) Determine x such that the probability that you wait less than x minutes is 0.50.” is broken down into a number of easy to follow steps, and 103 words. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. The full step-by-step solution to problem: 121E from chapter: 4.8 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM.

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