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

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,