Fundamentals of Differential Equations and Boundary Value Problems
7th Edition
ISBN: 9780321977106
Author: Nagle, R. Kent
Publisher: Pearson Education, Limited
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Chapter 6.1, Problem 13E
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8.1.6The yield of a chemical process is being studied. From previous experience, yield is known to be normally
distributed and σ = 3. The past 5 days of plant operation have
resulted in the following percent yields: 91.6, 88.75, 90.8, 89.95,
and 91.3. Find a 95% two-sided confidence interval on the true
mean yield.
8.1.7 .A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed
with σ = 0.001 millimeters. A random sample of 15 rings has a
mean diameter of x = 74.036 millimeters.
a. Construct a 99% two-sided confidence interval on the
mean piston ring diameter.
b. Construct a 99% lower-confidence bound on the mean
piston ring diameter. Compare the lower bound of this confi-
dence interval with the one in part (a).
8.1.2 .Consider the one-sided confidence interval expressions for a mean of a normal population.
a. What value of zα would result in a 90% CI?
b. What value of zα would result in a 95% CI?
c. What value of zα would result in a 99% CI?
8.1.3 A random sample has been taken from a normal distribution and the following confidence intervals constructed using the
same data: (38.02, 61.98) and (39.95, 60.05)
a. What is the value of the sample mean?
b. One of these intervals is a 95% CI and the other is a
90% CI. Which one is the 95% CI and why?
8.1.4 . A confidence interval estimate is desired for the gain
in a circuit on a semiconductor device. Assume that gain is normally distributed with standard deviation σ = 20.
a. How large must n be if the length of the 95% CI is to
be 40?
b. How large must n be if the length of the 99% CI is to
be 40?
8.1.5 Suppose that n = 100 random samples of water from
a freshwater lake were taken and the calcium concentration
(milligrams per liter) measured. A 95% CI on the mean calcium
concentration is 0.49 g μ g 0.82.
a. Would a 99% CI calculated from the same sample data be
longer or shorter?
b. Consider the following statement: There is a 95% chance
that μ is between 0.49 and 0.82. Is this statement correct?
Explain your answer.
c. Consider the following statement: If n = 100 random
samples of water from the lake were taken and the 95% CI on
μ computed, and this process were repeated 1000 times, 950
of the CIs would contain the true value of μ. Is this statement
correct? Explain your answer
Chapter 6 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - Prob. 7ECh. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...
Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - Using the Wronskian in Problems 15-18, verify that...Ch. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - Let L[y]:=y+y+xy, y1(x):=sinx, and y2(x):=x....Ch. 6.1 - Let L[y]:=yxy+4y3xy", y1(x)=cos2x, and y2(x):=1/3....Ch. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - Prob. 2ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - In Problems 15-18, find a general solution to the...Ch. 6.2 - Prob. 16ECh. 6.2 - In Problems 15 18, find a general solution to the...Ch. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - In Problems 1921, solve the given initial value...Ch. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - In Problems 22 and 23, find a general solution for...Ch. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Find a general solution to y3yy=0 by using Newtons...Ch. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Higher-Order Cauchy-Euler Equations. A...Ch. 6.2 - Prob. 32ECh. 6.2 - On a smooth horizontal surface, a mass of m1 kg is...Ch. 6.2 - Suppose the two springs in the coupled mass-spring...Ch. 6.2 - Vibrating Beam. In studying the transverse...Ch. 6.3 - In Problems 1-4, use the method of undetermined...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - In Problems 31-33, solve the given initial value...Ch. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Use the annihilator method to show that if f(x) in...Ch. 6.3 - Prob. 37ECh. 6.3 - In Problems 38 and 39, use the elimination method...Ch. 6.3 - Prob. 39ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 2ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Given that {x,x1,x4} is a fundamental solution set...Ch. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.RP - Determine the intervals for which Theorem 1 on...Ch. 6.RP - Determine whether the given functions are linearly...Ch. 6.RP - Show that the set of functions...Ch. 6.RP - Find a general solution for the given differential...Ch. 6.RP - Find a general solution for the homogeneous linear...Ch. 6.RP - Prob. 6RPCh. 6.RP - Prob. 7RPCh. 6.RP - Use the annihilator method to determine the form...Ch. 6.RP - Find a general solution to the Cauchy-Euler...Ch. 6.RP - Find a general solution to the given Cauchy-Euler...
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