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The number of large cracks in a length of pavement along a

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

Solution for problem 2SE Chapter 4

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 2SE

The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 m.

a. What is the probability that there will be exactly 8 cracks in a 500 m length of pavement?

b. What is the probability that there will be no cracks in a 100 m length of pavement?

c. Let T be the distance in meters between two successive cracks. What is the probability density function of 7?

d. What is the probability that the distance between two successive cracks will be more than 50 m?

Step-by-Step Solution:
Step 1 of 3

Solution 2SE

Step1 of 5:

Let us consider a random variable X it presents the number of large cracks in a length of pavement along a certain street and it has poisson distribution with mean of 1 crack per 100 m.

Let X follows poisson distribution with parameters “ ”.

Then the probability mass function of poisson distribution is given by:

, x = 0,1,2,...,n. 

Where,

= parameter

n = sample size

x = random variable

e = mathematical constant.

Here our goal is:

a).We need to find the probability that there will be exactly 8 cracks in a 500 m length of pavement.

b.We need to find the probability that there will be no cracks in a 100 m length of pavement.

c).We need to find the probability density function of 7, When T be the distance in meters between two successive cracks.

d).We need to find the probability that the distance between two successive cracks will be more than 50 m.

Step2 of 5:

a).

Here we have

             X = 8 and  

     =

                                                                = 5

Now,

The probability that there will be exactly 8 cracks in a 500 m length of pavement is given by

Consider,

                   

                              P(X = 8) =

 

                                  =

                                  =

                     

                                  = 0.0653

Hence, P(X = 8) = 0.0653.

Therefore, The probability that there will be exactly 8 cracks in a 500 m length of pavement is 0.0653.

Step3 of 5:

b).

Here we have

             X = 8 and  

     =

                                                                = 1

Now,

The probability that there will be no cracks in a 100 m length of pavement is given by

Consider,

 ...

Step 2 of 3

Chapter 4, Problem 2SE is Solved
Step 3 of 3

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

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 2SE from chapter: 4 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 full solution covers the following key subjects: cracks, Probability, length, Pavement, distance. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 2SE from 4 chapter was answered, more than 1386 students have viewed the full step-by-step answer. The answer to “The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 m.a. What is the probability that there will be exactly 8 cracks in a 500 m length of pavement?________________b. What is the probability that there will be no cracks in a 100 m length of pavement?________________c. Let T be the distance in meters between two successive cracks. What is the probability density function of 7?________________d. What is the probability that the distance between two successive cracks will be more than 50 m?” is broken down into a number of easy to follow steps, and 98 words.

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