Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4, Problem 7P
Use forward and backward difference approximations of
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In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a
random sample of 1014 adults aged 18 and over. One of the questions was, "How many
cups of coffee, if any, do you drink on an average day?" The following table shows the
results obtained (Gallup website, August 6, 2012).
Number of Cups
per Day
0
1
2
3
4 or more
Number of
Responses
365
264
193
91
101
Define a random variable x = number of cups of coffee consumed on an average day. Let
x=4 represent four or more cups.
a. Develop a probability distribution for x.
b. Compute the expected value of x.
c. Compute the variance of x.
d. Suppose we are only interested in adults who drink at least one cup of coffee on an
average day. For this group, let y = the number of cups of coffee consumed on an
average day. Compute the expected value of y and compare it to the expected value of x.
Ten major college football bowl games were played in January 2010, with the University
of Alabama beating the University of Texas 37 to 21 to become the national champion
of college football. The results of the 10 bowl games follow (USA Today, January 8, 2010).
Bowl Game
Score
Outback
Gator
Auburn 38 Northwestern 35
Florida State 33 West Virginia 21
Capital One
Penn State 19 LSU 17
Rose
Ohio State 26 Oregon 17
Florida 51 Cincinnati 24
Sugar
Cotton
Alamo
Fiesta
Mississippi State 21 Oklahoma State 7
Texas Tech 41 Michigan State 31
Boise State 17 TCU 10
Orange
Iowa 24 Georgia Tech 14
Championship
Alabama 37 Texas 21
Predicted
Point Margin
Actual
Point Margin
5
3
1
12
3
-2
14
3
9
-4
-3
4
229740706
14
10
10
16
The predicted winning point margin was based on Las Vegas betting odds approximately
one week before the bowl games were played. For example, Auburn was predicted to beat
Northwestern in the Outback Bowl by five points. The actual winning point margin for Au-
burn was three points. A…
In 2007 the New York Times reported that the median annual household income in the United
States was $55,500 (New York Times website, August, 21, 2013). Answer the following
questions based on the following sample of 14 household incomes for 2013 ($1000s).
49.4
52.2
52.4
53.4
51.3
52.1
48.7
64.5
51.6
46.5
52.9
52.5
52.1
51.2
a.
What is the median household income for the sample data for 2013?
b. Based on the sample data, estimate the percentage change in the median household
income from 2007 to 2013.
c. Compute the first and third quartiles.
Chapter 4 Solutions
Numerical Methods for Engineers
Ch. 4 - The following series can be used to approximate...Ch. 4 - 4.2 The Maclaurin series expansion for cos x...Ch. 4 - 4.3 Perform the same computation as in Prob. 4.2,...Ch. 4 - 4.4 The Maclaurin series expansion for the...Ch. 4 - 4.5 Use zero- through third-order Taylor series...Ch. 4 - 4.6 Use zero- through fourth-order Taylor series...Ch. 4 - Use forward and backward difference approximations...Ch. 4 - 4.8 Use a centered difference approximation of to...Ch. 4 - 4.9 The Stefan-Boltzmann law can be employed to...Ch. 4 - Repeat Prob. 4.9 but for a copper sphere with...
Ch. 4 - Recall that the velocity of the falling...Ch. 4 - 4.12 Repeat Prob. 4.11 with.
Ch. 4 - 4.13 Evaluate and interpret the condition numbers...Ch. 4 - Employing ideas from Sec. 4.2, derive the...Ch. 4 - Prove that Eq. (4.4) is exact for all values of x...Ch. 4 - Mannings formula for a rectangular channel can be...Ch. 4 - If |x|1, it is known that 11x=1+x+x2+x3+ Repeat...Ch. 4 - A missile leaves the ground with an initial...Ch. 4 - To calculate a planets space coordinates, we have...Ch. 4 - 4.20 Consider the function on the interval . Use...Ch. 4 - Derive Eq. (4.31).Ch. 4 - 4.22 Repeat Example 4.8, but for .
Ch. 4 - 4.23 Repeat Example 4.8, but for the forward...Ch. 4 - 4.24 Develop a well-structured program to compute...
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