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Devore-Probability&Statistics for Engineering 8/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 35 / 59

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving...  ()

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Question
Points
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Total
35/59 (59.3%)

  • Instructions

    This comprehensive introduction to probability and statistics will give students the solid grounding they need no matter what their engineering specialty. Probability and Statistics for Engineering and the Sciences 8th edition emphasizes concepts, models, methodology, and applications that facilitate students’ understanding. The WebAssign component for this text engages students with immediate feedback, lecture videos, and a question bank of end-of-section exercises.

    In this assignment we present several textbook question types found in Probability and Statistics for Engineering and the Sciences 8/e by Jay Devore, published by Cengage Learning.

    All questions in the demo assignment feature Read it links.

    Click here for a list of all of the questions coded in WebAssign. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. –/6 points DevoreStat8 4.E.004. My Notes
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Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Use the Rayleigh distribution, with the following pdf as a model for the X distribution.
f(x;Theta)={(x/Theta^2 middot e^(-x^2\/ \(2Theta^2 \))text( )x>0,0 text( otherwise))
(a) Explain how you would verify that f(x; θ) is a legitimate pdf.

This answer has not been graded yet.




(b) Suppose θ = 107. What is the probability that X is at most 200?


What is the probability that X is less than 200?


What is the probability that X is at least 200?


(c) What is the probability that X is between 100 and 200 (again assuming θ = 107)?


(d) Give an expression for P(X x). (Hint: Use theta for θ and x for x, as appropriate. Give the result of integration.)


You may need to use the appropriate table in the Appendix of Tables to answer this question.
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2. –/8 points DevoreStat8 4.E.022. My Notes
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–/8
 
The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with the following pdf.
f(x)={(4*(3/4-1/x^2) text()1<=x<=2, 0 text(otherwise))
(a) Compute the cdf of X.
F(x)={( , , , , , )
x<1
1<=x<=2
2<x

(b) Obtain an expression for the (100p)th percentile.


What is the value of ?


(c) Compute E(X) and V(X).
E(X) =
V(X) =

(d) If 1.5 thousand gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the 1.5 thousand gallons is expected to be left at the end of the week? [Hint: Let h(x) = amount left when demand = x.]


You may need to use the appropriate table in the Appendix of Tables to answer this question.
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3. –/5 points DevoreStat8 4.E.029. My Notes
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Let Z be a standard normal random variable. In each case, determine the value of the constant c that makes the probability statement correct.
(a) (c) = 0.9846


(b) P(0 Z c) = 0.2967


(c) P(c Z) = 0.1292


(d) P(-c Z c) = 0.6528


(e) P(c |Z|) = 0.0135


You may need to use the appropriate table in the Appendix of Tables to answer this question.
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4. –/3 points DevoreStat8 4.E.040. My Notes
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It has been suggested that yield strength (ksi) for A36 grade steel is normally distributed with mu = 44 and σ = 3.0.
(a) What is the probability that yield strength is at most 40?


What is the probability that yield strength is greater than 60?


(b) What yield strength value separates the strongest 75% from the others?
ksi


You may need to use the appropriate table in the Appendix of Tables to answer this question.
Your work in question(s) will also be submitted or saved.
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5. –/4 points DevoreStat8 4.E.066. My Notes
Question Part
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Suppose the time spent by a randomly selected student who uses a terminal connected to a local time-sharing computer facility has a gamma distribution with mean 22.5 min and variance 101.25 min2.
(a) What are the values of α and β?
α =
β =

(b) What is the probability that a student uses the terminal for at most 24 min?


(c) What is the probability that a student spends between 20 and 40 min using the terminal?


You may need to use the appropriate table in the Appendix of Tables to answer this question.
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6. –/33 points DevoreStat8 4.E.089. My Notes
Question Part
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Dataset ex04-89 is available here.
Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint. ("Achieving a Target Value for a Manufacturing Process: A Case Study," J. of Quality Technology, 1992: 22-26).(Do this on paper. Your instructor may ask you to turn in this work.)
0.83
 0.88
 0.88
 1.04
 1.09
 1.12
 1.29
 1.31
1.48
 1.49
 1.59
 1.62
 1.65
 1.71
 1.76
 1.83
Percentage
z percentile
Percentage
z percentile
Would you feel comfortable estimating population mean thickness using a method that assumed a normal population distribution?
    


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