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Chapter 4: Q122E (page 269)

Shear strength of rock fractures. Understanding the characteristics

of rock masses, especially the nature of the fracturesis essential when building dams and power plants.The shear strength of rock fractures was investigated inEngineering Geology(May 12, 2010). The Joint RoughnessCoefficient (JRC) was used to measure shear strength.Civil engineers collected JRC data for over 750 rock fractures.The results (simulated from information provided in the article) are summarized in the accompanying SPSShistogram. Should the engineers use the normal probabilitydistribution to model the behavior of shear strength forrock fractures? Explain

Short Answer

Expert verified

Engineers should use the normal probability distribution to model the behavior of shear strength for rock fractures

Step by step solution

01

Given Information

The histograms for 750 rock fractures is given,

02

Explanation

From the above histogram, it is seen that the histogram looks like a normal probability curve. So, the engineers can use normal distribution to model the behavior of shear strength for rock fractures.

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Most popular questions from this chapter

Find az-score, call itz0, such that

a.P(z鈮�z0)=.5080

b.P(z鈮�z0)=.5517

c.P(z鈮�z0)=.1492

d.P(z0鈮�z鈮�.59)=.4773

Find each of the following probabilities for the standard normal random variable z:

a.P(-鈮�z鈮�1)b.P(-1.96鈮�z鈮�1.96)c.P(-1645鈮�z鈮�1.645)d.P(-2鈮�z鈮�2)

Privacy and information sharing. Refer to the Pew Internet & American Life Project Survey (January 2016), Exercise 4.48 (p. 239). The survey revealed that half of all U.S. adults would agree to participate in a free cost-saving loyalty card program at a grocery store, even if the store could potentially sell these data on the customer鈥檚 shopping habits to third parties. In a random sample of 250 U.S. adults, let x be the number who would participate in the free loyalty card program.

a. Find the mean of x. (This value should agree with your answer to Exercise 4.48c.)

b. Find the standard deviation of x.

c. Find the z-score for the value x = 200.

d. Find the approximate probability that the number of the 250 adults who would participate in the free loyalty card program is less than or equal to 200.

Consider the probability distributions shown here:

  1. Use your intuition to find the mean for each distribution. How did you arrive at your choice?
  2. Which distribution appears to be more variable? Why?
  3. Calculate渭鈥塧苍诲鈥壪�2 for each distribution. Compare these answers with your answers in parts a and b.

The binomial probability distribution is a family of probability distributions with every single distribution depending on the values of n and p. Assume that x is a binomial random variable with n = 4.

  1. Determine a value of p such that the probability distribution of x is symmetric.
  2. Determine a value of p such that the probability distribution of x is skewed to the right.
  3. Determine a value of p such that the probability distribution of x is skewed to the left.
  4. Graph each of the binomial distributions you obtained in parts a, b, and c. Locate the mean for each distribution on its graph.\
  5. In general, for what values of p will a binomial distribution be symmetric? Skewed to the right? Skewed to the left?
See all solutions

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