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An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Textbook Question
Chapter 4.4, Problem 1Q
Because of her past convictions for mail fraud and forgery, Jody has a 30% chance each year of having her tax returns audited. What is the
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Cycles to
failure
Position in
ascending
order
0.5
f(x))
(x;)
Problem 44
Marsha, a renowned cake scientist, is trying to determine how long different cakes can survive intense fork attacks before collapsing into crumbs.
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Construct P-P plots for (a.) a normal distribution, (b.) a lognormal distribution, and (c.) a Weibull distribution (using the information included in the
table below). Which distribution seems to be the best model for the cycles to failure for this material? Explain your answer in detail.
Observation
Empirical
cumulative
Probability distribution
Cumulative distribution
Inverse of cumulative
distribution F-1 (-0.5)
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(S)
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3
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5
2
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7
7
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Normal…
Problem 3
In their lab, engineer Daniel and Paulina are desperately trying to perfect time travel. But the problem is that
their machine still struggles with power inconsistencies-sometimes generating too little energy, other times
too much, causing unstable time jumps. To prevent catastrophic misjumps into the Jurassic era or the far
future, they must calibrate the machine's power output. After extensive testing, they found that the time
machine's power output follows a normal distribution, with an average energy level of 8.7 gigawatts and a
standard deviation of 1.2 gigawatts.
The Time Travel Safety Board has set strict guidelines: For a successful time jump, the
machine's power must be between 8.5 and 9.5 gigawatts. What is the probability that a randomly
selected time jump meets this precision requirement?
Daniel suggests that adjusting the mean power output could improve time-travel accuracy.
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Problem 5 (
Marybeth is also interested in the experiment from Problem 2 (associated with the enhancements for Captain
America's shield), so she decides to start a detailed literature review on the subject. Among others, she found
a paper where they used a 2"(4-1) fractional factorial design in the factors: (A) shield material, (B) throwing
mechanism, (C) edge modification, and (D) handle adjustment. The experimental design used in the paper is
shown in the table below.
a.
Run
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B
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D
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-1
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1
4
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1
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paper?
s) What was the generator used in the 2"(4-1) fractional factorial design described in the
b.
Based on the resolution of this design, what do you think about the generator used in the
paper? Do you think it was a good choice, or would you have selected a different one? Explain your
answer in detail.
Chapter 4 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 4.2 - If a typist averages one misspelling in every 3250...Ch. 4.2 - A medical study recently documented that 905...Ch. 4.2 - Five hundred people are attending the first annual...Ch. 4.2 - A chromosome mutation linked with colorblindness...Ch. 4.2 - Suppose that 1% of all items in a supermarket are...Ch. 4.2 - A newly formed life insurance company has...Ch. 4.2 - According to an airline industry report (189),...Ch. 4.2 - Electromagnetic fields generated by power...Ch. 4.2 - Astronomers estimate that as many as one hundred...Ch. 4.2 - During the latter part of the nineteenth century,...
Ch. 4.2 - A random sample of three hundred fifty-six seniors...Ch. 4.2 - Midwestern Skies books ten commuter flights each...Ch. 4.2 - Prob. 13QCh. 4.2 - Prob. 14QCh. 4.2 - Prob. 15QCh. 4.2 - A tool and die press that stamps out cams used in...Ch. 4.2 - In a new fiber-optic communication system,...Ch. 4.2 - Assume that the number of hits, X, that a...Ch. 4.2 - Prob. 19QCh. 4.2 - Suppose a radioactive source is metered for two...Ch. 4.2 - Suppose that on-the-job injuries in a textile mill...Ch. 4.2 - Find P(X=4) if the random variable X has a Poisson...Ch. 4.2 - Prob. 23QCh. 4.2 - Prob. 24QCh. 4.2 - Prob. 25QCh. 4.2 - Prob. 26QCh. 4.2 - Records show that deaths occur at the rate of 0.1...Ch. 4.2 - Fifty spotlights have just been installed in an...Ch. 4.2 - Prob. 29QCh. 4.3 - Use Appendix Table A.1 to evaluate the following...Ch. 4.3 - Let Z be a standard normal random variable. Use...Ch. 4.3 - (a) Let 0ab. Which number is larger?...Ch. 4.3 - Prob. 4QCh. 4.3 - Assume that the random variable Z is described by...Ch. 4.3 - Prob. 6QCh. 4.3 - Prob. 7QCh. 4.3 - Hertz Brothers, a small, family-owned radio...Ch. 4.3 - Prob. 9QCh. 4.3 - State Techs basketball team, the Fighting...Ch. 4.3 - A random sample of 747 obituaries published...Ch. 4.3 - Prob. 12QCh. 4.3 - If pX(k)=(10k)(0.7)k(0.3)10k,k=0,1,10, is it...Ch. 4.3 - A sell-out crowd of 42,200 is expected at...Ch. 4.3 - A fair coin is tossed two hundred times. Let Xi=1...Ch. 4.3 - Suppose that one hundred fair dice are tossed....Ch. 4.3 - Let X be the amount won or lost in betting $5 on...Ch. 4.3 - Prob. 18QCh. 4.3 - An electronics firm receives, on the average,...Ch. 4.3 - Prob. 20QCh. 4.3 - Econo-Tire is planning an advertising campaign for...Ch. 4.3 - A large computer chip manufacturing plant under...Ch. 4.3 - Prob. 23QCh. 4.3 - Prob. 24QCh. 4.3 - A criminologist has developed a questionnaire for...Ch. 4.3 - The cross-sectional area of plastic tubing for use...Ch. 4.3 - At State University, the average score of the...Ch. 4.3 - A college professor teaches Chemistry 101 each...Ch. 4.3 - Suppose the random variable Y can be described by...Ch. 4.3 - It is estimated that 80% of all eighteen-year-old...Ch. 4.3 - Prob. 31QCh. 4.3 - Prob. 32QCh. 4.3 - The IQs of nine randomly selected people are...Ch. 4.3 - Let Y1,Y2,...,Yn be a random sample from a normal...Ch. 4.3 - A circuit contains three resistors wired in...Ch. 4.3 - Prob. 36QCh. 4.3 - Use moment-generating functions to prove the two...Ch. 4.3 - Let Y1,Y2,...,Y9 be a random sample of size 9 from...Ch. 4.3 - Prob. 39QCh. 4.4 - Because of her past convictions for mail fraud and...Ch. 4.4 - A teenager is trying to get a drivers license....Ch. 4.4 - Prob. 3QCh. 4.4 - Recently married, a young couple plans to continue...Ch. 4.4 - Show that the cdf for a geometric random variable...Ch. 4.4 - Suppose three fair dice are tossed repeatedly. Let...Ch. 4.4 - Prob. 7QCh. 4.4 - Sometimes the geometric random variable is defined...Ch. 4.4 - Prob. 9QCh. 4.4 - Suppose that the random variables X1 and X2 have...Ch. 4.5 - A door-to-door encyclopedia salesperson is...Ch. 4.5 - An underground military installation is fortified...Ch. 4.5 - Darryls statistics homework last night was to flip...Ch. 4.5 - When a machine is improperly adjusted, it has...Ch. 4.5 - For a negative binomial random variable whose pdf...Ch. 4.5 - Let the random variable X denote the number of...Ch. 4.5 - Calculate the mean, variance, and...Ch. 4.5 - Let X1,X2, and X3 be three independent negative...Ch. 4.5 - Differentiate the moment-generating function...Ch. 4.5 - Suppose that X1,X2,...,Xk are independent negative...Ch. 4.6 - An Arctic weather station has three electronic...Ch. 4.6 - A service contact on a new university computer...Ch. 4.6 - Suppose a set of measurements Y1,Y2,...,Y100 is...Ch. 4.6 - Demonstrate that plays the role of a scale...Ch. 4.6 - Show that a gamma pdf has the unique mode r1; that...Ch. 4.6 - Prove that (12)=. (Hint: Consider E(Z2)), where Z...Ch. 4.6 - Show that (72)=158.Ch. 4.6 - If the random variable Y has the gamma pdf with...Ch. 4.6 - Differentiate the gamma moment-generating function...Ch. 4.6 - Prob. 10Q
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