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Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset Vaia Explanations$ Math

13th Edition · 888 pages

ISBN: 9780134506593

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

Preventative maintenance tests. The optimal schedulingofpreventative maintenance tests of some (but not all) ofnindependently operating components was developed in Reliability Engineering and System Safety(January $2006$ ).The time (in hours) between failures of a component wasapproximated by an exponential distribution with mean $θ$ .

a. Suppose $θ = 1000$ hours. Find the probability that the time between component failures ranges between $1200$ and $1500$ hours.

b. Again, assume $θ = 1000$ hours. Find the probability that the time between component failures is at least $1200$ hours.

c. Given that the time between failures is at leastrole="math" localid="1658214710824" $1200$ hours, what is the probability that the time between failures is less than $1500$ hours?

Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of the power quality of a transformer, Exercise 2.127 (p. 132). Recall that two causes of poor power quality are “sags” and “swells.”. (A sag is an unusual dip, and a swell is an unusual increase in the voltage level of a transformer.) For Turkish transformers built for heavy industry, the mean number of sags per week was 353, and the mean number of swells per week was 184. As in Exercise 2.127, assume the standard deviation of the sag distribution is 30 sags per week, and the standard deviation of the swell distribution is 25 swells per week. Also, assume that the number of sags and number of swells is both normally distributed. Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week.

a. What is the probability that the number of sags per week is less than 400?

b. What is the probability that the number of swells per week is greater than 100?

4.139 Load on timber beams. Timber beams are widely used inhome construction. When the load (measured in pounds) perunit length has a constant value over part of a beam, the loadis said to be uniformly distributed over that part of the beam.Uniformly distributed beam loads were used to derive thestiffness distribution of the beam in the American Institute of

Aeronautics and Astronautics Journal(May 2013). Considera cantilever beam with a uniformly distributed load between100 and 115 pounds per linear foot.

a. What is the probability that a beam load exceeds110 pounds per linearfoot?

b. What is the probability that a beam load is less than102 pounds per linear foot?

c. Find a value Lsuch that the probability that the beamload exceeds Lis only .1.

Cell phone handoff behavior. Refer to the Journal of Engineering, Computing and Architecture (Vol. 3., 2009) study of cell phone handoff behavior, Exercise 3.47 (p. 183). Recall that a “handoff” describes the process of a cell phone moving from one base channel (identified by a color code) to another. During a particular driving trip, a cell phone changed channels (color codes) 85 times. Color code “b” was accessed 40 times on the trip. You randomly select 7 of the 85 handoffs. How likely is it that the cell phone accessed color code “b” only twice for these 7 handoffs?

Assume that xis a random variable best described by a uniform distribution with $c = 10$ and $d = 90$ .

a. Find $f (x)$ .

b. Find the mean and standard deviation of x.

c. Graph the probability distribution for xand locate its mean and theintervalon the graph.

d. Find $P (x \leq 60)$ .

e. Find $P (x \geq 90)$ .

f. Find $P (x \leq 80)$ .

g. Find $P (μ - σ \leq x \leq μ + σ)$ .

h. Find $P (x > 75)$ .

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