The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile.a. determine the probability mass function of the number of cracks (x) in 5 miles away.b. Find the probability that there are at least five cracks in 5 miles of highway that require repair.c. calculate the mean and variance of X. 2. Find the probability that there are at least five cracks in 5 miles ofhighway that require repair.3. Calculate the mean and variance of X. Exercise 5.6 The number of cracks that need repair in a section of interstate highwayfollows a Poisson distribution with a mean of two cracks per mile.1. Determine the probability mass function of the number of cracks (X) in5 miles of highway.

Given Information Mean = 2 cracks per mile Number of cracks in 5 miles

Answered: The number of cracks in a section of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile.

a. determine the probability mass function of the number of cracks (x) in 5 miles away.
b. Find the probability that there are at least five cracks in 5 miles of highway that require repair.
c. calculate the mean and variance of X.

2. Find the probability that there are at least five cracks in 5 miles of
highway that require repair.
3. Calculate the mean and variance of X.

Exercise 5.6 The number of cracks that need repair in a section of interstate highway
follows a Poisson distribution with a mean of two cracks per mile.
1. Determine the probability mass function of the number of cracks (X) in
5 miles of highway.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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