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Devore-Probability&Statistics for Engineering 7/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 10 / 64

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

Last Saved : n/a Saving...  ()

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4/5 1/6 5/8 –/3 –/5 –/4 –/33
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10/64 (15.6%)

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1. 4/5 points  |  Previous Answers DevoreStat7 4.AE.014. My Notes
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4/5
 
Example 4.14 The 99th percentile of the standard normal distribution is that value on the horizontal axis such that the area under the z curve to the Correct: Your answer is correct. of the value is Incorrect: Your answer is incorrect. . Appendix Table A.3 gives for fixed z the area under the standard normal curve to the left of z, whereas here we have the area and want the value of z. This is the "inverse" problem to P(Z z) = ? so the table is used in an inverse fashion: Find in the middle of the table .9900; the row and column in which it lies identify the 99th z percentile. Here .9901 lies at the intersection of the row marked 2.3 and column marked .03, so the Correct: Your answer is correct. th percentile is (approximately) z = Correct: Your answer is correct. . (See Figure 4.17.) By symmetry, the first percentile is as far below 0 as the 99th is above 0, so equals Correct: Your answer is correct. (1% lies below the first and also above the 99th). (See Figure 4.18.)


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2. 1/6 points  |  Previous Answers DevoreStat7 4.P.004. My Notes
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1/6
 
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.

Score: 1 out of 1

Comment:




(b) Suppose θ = 140. 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 = 140)?


(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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3. 5/8 points  |  Previous Answers DevoreStat7 4.P.022. My Notes
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1/1 1/1 1/1 0/1 –/1 1/1 1/1 0/1
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5/8
 
The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with the following pdf.
f(x)={(2*(1-1/x^2) text()1<=x<=2, 0 text(otherwise))
(a) Compute the cdf of X.
F(x)={( , , , , , )
0
Correct: Your answer is correct. 		x<1
(2x+2x​)−4
Correct: Your answer is correct. 		1<=x<=2
1
Correct: Your answer is correct. 		2<x

(b) Obtain an expression for the (100p)th percentile.
1+p4 ​+√p(8+p)
Incorrect: Your answer is incorrect.

What is the value of ?


(c) Compute E(X) and V(X).
E(X) = Correct: Your answer is correct.
V(X) = Correct: Your answer is correct.

(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.]
Incorrect: Your answer is incorrect.


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4. –/3 points DevoreStat7 4.P.040. My Notes
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–/3
 
It has been suggested that yield strength (ksi) for A36 grade steel is normally distributed with mu = 43 and σ = 3.5.
(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.

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5. –/5 points DevoreStat7 4.P.061. My Notes
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–/5
 
Extensive experience with fans of a certain type used in diesel engines has suggested that the exponential distribution provides a good model for time until failure. Suppose the mean time until failure is 27,600 hours.
(a) What is the probability that a randomly selected fan will last at least 20,000 hours?


What is the probability that a randomly selected fan will last at most 30,000 hours?


What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?


(b) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?


What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?


You may need to use the appropriate table in the Appendix of Tables to answer this question.

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6. –/4 points DevoreStat7 4.P.066. My Notes
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–/1 –/1 –/1 –/1
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–/4
 
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 10.5 min and variance 36.75 min 2.
(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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7. –/33 points DevoreStat7 4.P.089. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
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–/33
 
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?
    


You may need to use the appropriate table in the Appendix of Tables to answer this question.

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