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The distance between flaws on a long cable is

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 4E Chapter 4.7

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

The distance between flaws on a long cable is exponentially distributed with mean 12 m.

a. Find the probability that the distance between two flaws is greater than 15 m.

b. Find the probability that the distance between two flaws is between 8 and 20 m.

c. Find the median distance.

d. Find the standard deviation of the distances.

e. Find the 65th percentile of the distances.

Step-by-Step Solution:

Step 1 of 6</p>

In a long cable the distance between flaws is exponentially distributed with mean 12 m

The mean of exponential distribution is=12

                                                         Then =0.0833

The pmf of Exponential distribution is

The CDF of exponential distribution is

Step 2 of 6</p>

a) We have to find the probability that the distance is greater than 15 m

Then P(X>15)=1-P(X15)

                                =1-(1-)

                   =

                =0.2866

Hence the probability that the distance is greater than 15 m is 0.2866

Step 3 of 6</p>

b) We have to find the probability that the distance is between 8 and 20 meters

Then P(8=P(X

                                             =(1-)-(1-)

                                  =-

                          =

                   =0.5136 - 0.189

        =0.3246

Hence the probability that the distance is between 8 and 20 meters is 0.3246

Step 4 of 6

Chapter 4.7, Problem 4E is Solved
Step 5 of 6

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The answer to “The distance between flaws on a long cable is exponentially distributed with mean 12 m.a. Find the probability that the distance between two flaws is greater than 15 m.________________b. Find the probability that the distance between two flaws is between 8 and 20 m.________________c. Find the median distance.________________d. Find the standard deviation of the distances.________________e. Find the 65th percentile of the distances.” is broken down into a number of easy to follow steps, and 62 words. This full solution covers the following key subjects: Find, distance, flaws, distances, Probability. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 4E from 4.7 chapter was answered, more than 1457 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 4E from chapter: 4.7 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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