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Devore-Prob.&Stats for Eng. International 8/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 39 / 44

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

Last Saved : n/a Saving...  ()

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Question
Points
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–/8 –/6 –/5 –/3 –/4 –/18
Total
39/44 (88.6%)

  • Instructions

    Create your course assignments by selecting questions from our 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 International Edition 8/e by Jay Devore, published by Brooks/Cole. 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. –/8 points DevoreStatINT8 4.E.004. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
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–/8
 
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 pdf
f(x; θ) = 
x
θ2
 · e−x2/(2θ2)		    x > 0
0    otherwise
as a model for the X distribution.
(a) Verify that f(x; θ) is a legitimate pdf.
∞
x
θ2
 · e−x2/(2θ2)
0
 dx
 		=
∞
0
=
0 − 
=

(b) Suppose θ = 137. What is the probability that X is at most 200? Less than 200? At least 200? (Round your answer to four decimal places.)
at most 200
less than 200    
at least 200

(c) What is the probability that X is between 100 and 200 (again assuming θ = 137)? (Round your answer to four decimal places.)


(d) Give an expression for P(X ≤ x).
P(X ≤ x) =
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2. –/6 points DevoreStatINT8 4.E.022. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50
Total
–/6
 
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
x2
    1 ≤ x ≤ 2
0otherwise
(a) Compute the cdf of X.
F(x) = 
 		    0 x < 1
1 ≤ x ≤ 2
    1 2 > x

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


What is the value of mu tilde? (Round your answer to three decimal places.)


(c) Compute E(X) and V(X). (Round your answers to four decimal places.)
E(X) = thousand gallons
V(X) = thousand gallons squared

(d) If 1.4 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 1.4 thousand gallons is expected to be left at the end of the week? [Hint: Let h(x) = amount left when demand = x.] (Round your answer to three decimal places.)
thousand gallons
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3. –/5 points DevoreStatINT8 4.E.029. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50
Total
–/5
 
In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.)
(a)    Φ(c) = 0.9830


(b)    P(0 ≤ Z ≤ c) = 0.2939


(c)    P(c ≤ Z) = 0.1210


(d)    P(−c ≤ Z ≤ c) = 0.6528


(e)    P(c ≤ |Z|) = 0.0128

You may need to use the appropriate table in the Appendix of Tables to answer this question.
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4. –/3 points DevoreStatINT8 4.E.040. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/50 0/50 0/50
Total
–/3
 
An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 43 and σ = 5.0.
(a) What is the probability that yield strength is at most 38? Greater than 61? (Round your answers to four decimal places.)
at most 38     
greater than 61

(b) What yield strength value separates the strongest 75% from the others? (Round your answer to three decimal places.)
ksi

You may need to use the appropriate table in the Appendix of Tables to answer this question.
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5. –/4 points DevoreStatINT8 4.E.066. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50
Total
–/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 15 min and variance 45 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 21 min? (Round your answer to three decimal places.)


(c) What is the probability that a student spends between 12 and 30 min using the terminal? (Round your answer to three decimal places.)

You may need to use the appropriate table in the Appendix of Tables to answer this question.
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6. –/18 points DevoreStatINT8 4.E.093. 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
–/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
Total
–/18
 
Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint.
0.85 0.87 0.89 1.04 1.11 1.14 1.30 1.30
1.48 1.51 1.59 1.63 1.66 1.70 1.77 1.82
Determine the z percentile associated with each sample observation. (Round your answers to two decimal places.)
Sample observation 0.85 0.87 0.89 1.04 1.11 1.14 1.30 1.30
z percentile
   
Sample observation 1.48 1.51 1.59 1.63 1.66 1.70 1.77 1.82
z percentile

Choose the plot that best represents the normal probability plot for the sample of observations.


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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