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

James Finch

Statistics, Fall 2010

Instructor: Dr. Friendly

Current Score: 18/64

Due: Saturday, October 23, 2010 22:00 EDT

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Question
Points
1 2 3 4 5 6 7
5 6 7/8 0/3 0/5 0/4 0/33
Total
18/64

Description

Here are some textbook questions from Probability and Statistics for Engineering and the Sciences 7/e by Jay L. Devore published by Brooks/Cole Publishing. Click here for a list of all of the questions coded in WebAssign.


Instructions

This demo assignment allows many submissions and allows you to try another version of the same question for practice.



1. 5/5 points All Submissions Notes Question: DevoreStat7 4.AE.014.
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Example 4.14The 99th percentile of the standard normal distribution is that value on the horizontal axis such that the area under the z curve to the Your answer is correct. of the value is
Enter an exact number.
Your answer is correct.. 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
Enter an exact number.
Your answer is correct.th percentile is (approximately) z =
Enter an exact number.
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
Enter an exact number.
Your answer is correct. (1% lies below the first and also about the 99th). (See Figure 4.18.)

2. 6/6 points All Submissions Notes Question: DevoreStat7 4.P.004.
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2/50 2/50 2/50 2/50 2/50 3/50
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6/6
 
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.



(b) Suppose θ = 140. What is the probability that X is at most 200?
Enter a number.
Your answer is correct.

What is the probability that X is less than 200?
Enter a number.
Your answer is correct.

What is the probability that X is at least 200?
Enter a number.
Your answer is correct.

(c) What is the probability that X is between 100 and 200 (again assuming θ = 140)?
Enter a number.
Your answer is correct.

(d) Give an expression for P(X x). (Hint: Use theta for θ and x for x, as appropriate. Give the result of integration.)
<math><mrow><mn>1</mn><mo>-</mo><msup><mi>e</mi><mrow><mo>-</mo><mfrac><msup><mi>x</mi><mn>2</mn></msup><mrow><mn>2</mn><mo>&space;</mo><msup><mi>&theta;</mi><mn>2</mn></msup></mrow></mfrac></mrow></msup></mrow></math> Your answer is correct.

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3. 7/8 points All Submissions Notes Question: DevoreStat7 4.P.022.
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1 2 3 4 5 6 7 8
1 1 1 1 1 1 1 0/1
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7/8
 
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)={( , , , , , ) <math><mrow><mn>0</mn></mrow></math> Your answer is correct.x<1
<math><mrow><mn>2</mn><mfenced close=")" open="("><mo>-</mo><mn>2</mn><mo>+</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>+</mo><mi>x</mi></mfenced></mrow></math> Your answer is correct.1<=x<=2
<math><mrow><mn>1</mn></mrow></math> Your answer is correct.2<x

(b) Obtain an expression for the (100p)th percentile.
<math><mrow><mfrac><mfenced close=")" open="("><mn>4</mn><mo>+</mo><mi>p</mi><mo>+</mo><msqrt><mi>p</mi></msqrt><mo>*</mo><msqrt><mi>p</mi><mo>+</mo><mn>8</mn></msqrt></mfenced><mn>4</mn></mfrac></mrow></math> Your answer is correct.

What is the value of ?
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Your answer is correct.

(c) Compute E(X) and V(X).
E(X) =
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Your answer is correct.
V(X) =
Enter a number.
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.]
Enter a number.

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4. 0/3 points All Submissions Notes Question: DevoreStat7 4.P.040.
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0/3
 
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?
Enter a number.
Your answer is incorrect.

What is the probability that yield strength is greater than 60?
Enter a number.
Your answer is incorrect.

(b) What yield strength value separates the strongest 75% from the others?
Enter a number.
Your answer is incorrect. ksi

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5. –/5 points Notes Question: DevoreStat7 4.P.061.
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0/1 0/1 0/1 0/1 0/1
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0/5
 
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?
Enter a number.


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


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


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


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

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6. –/4 points Notes Question: DevoreStat7 4.P.066.
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0/4
 
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 =
Enter a number.
β =
Enter a number.

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


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

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7. –/33 points Notes Question: DevoreStat7 4.P.089.
Question part
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0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1
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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0/33
 
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
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z percentile
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Percentage
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z percentile
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Would you feel comfortable estimating population mean thickness using a method that assumed a normal population distribution?
    


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