Discrete Mathematics With Applications
5th Edition
ISBN: 9781337694193
Author: EPP, Susanna S.
Publisher: Cengage Learning,
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Chapter 11.2, Problem 20ES
To determine
The proof for the given statement.
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Table 5: Measurement Data for Question 9
Part Number
Op-1, M-1
Op-1, M-2 | Op-2, M-1 Op-2, M-2 | Op-3, M-1
Op-3, M-2
1
21
20
20
20
19
21
2
24
23
24
24
23
24
3
4
5
6
7
8
9
10
11
21
12
8222332
201
21
20
22
20
22
27
27
28
26
27
28
19
18
19
21
24
21
22
19
17
18
24
23
25
25
23
26
20
20
18
19
17
13
23
25
25
2 3 3 3 3 2 3
18
18
21
21
23
22
24
22
20
19
23
24
25
24
20
21
19
18
25
25
14
24
24
23
25
24
15
29
30
30
28
31
16
26
26
25
26
25
17
20
20
19
20
20
843882388
20
18
25
20
19
25
25
30
27
20
18
19
21
19
19
21
23
19
25
26
25
24
25
25
20
19
19
18
17
19
17
Question 9
A measurement systems experiment involving 20 parts, three operators (Op-1, Op-2, Op-3), and two measure-
ments (M-1, M-2) per part is shown in Table 5.
(a) Estimate the repeatability and reproducibility of the gauge.
(b) What is the estimate of total gauge variability?"
(c) If the product specifications are at LSL = 6 and USL 60, what can you say about gauge capability?
Question 5
A fraction nonconforming control chart with center line 0.10, UCL = 0.19, and LCL = 0.01 is used to control a
process.
(a) If three-sigma limits are used, find the sample size for the control charte
2
(b) Use the Poisson approximation to the binomial to find the probability of type I error.
(c) Use the Poisson approximation to the binomial to find the probability of type II error if the process fraction
defective is actually p = 0.20.
Question 8
Ten parts are measured three times by the same operator in a gauge capability study. The data are shown in
Table 4.
(a) Describe the measurement error that results from the use of this gauge. I
(b) Estimate total variability and product variability.
(c) What percentage of total variability is due to the gauge?
(d) If specifications on the part are at 100±15, find the P/T ratio for this gauge. Comment on the adequacy
of the gauge.
3
Table 4: Measurement Data for Question 8
Part Number Measurement 1 Measurement 2 Measurement 3
1
2
100
95
101
100
93
97
3
101
103
100
4
96
95
97
5
98
98
96
6
99
98
98
7889
95
97
98
100
99
98
100
100
97
10
100
98
98
99
Chapter 11 Solutions
Discrete Mathematics With Applications
Ch. 11.1 - If f is a real-valued function of a real variable,...Ch. 11.1 - Prob. 2TYCh. 11.1 - Prob. 3TYCh. 11.1 - Prob. 4TYCh. 11.1 - Prob. 5TYCh. 11.1 - Prob. 6TYCh. 11.1 - Prob. 1ESCh. 11.1 - The graph of a function g is shown below. a. Is...Ch. 11.1 - Prob. 3ESCh. 11.1 - Sketch the graphs of the power functions p3 and p4...
Ch. 11.1 - Prob. 5ESCh. 11.1 - Prob. 6ESCh. 11.1 - Prob. 7ESCh. 11.1 - Sketch a graph for each of the functions defined...Ch. 11.1 - Prob. 9ESCh. 11.1 - Prob. 10ESCh. 11.1 - Prob. 11ESCh. 11.1 - Prob. 12ESCh. 11.1 - Prob. 13ESCh. 11.1 - The graph of a function f is shown below. Find the...Ch. 11.1 - Prob. 15ESCh. 11.1 - Prob. 16ESCh. 11.1 - Prob. 17ESCh. 11.1 - Prob. 18ESCh. 11.1 - Prob. 19ESCh. 11.1 - Prob. 20ESCh. 11.1 - Prob. 21ESCh. 11.1 - Prob. 22ESCh. 11.1 - Prob. 23ESCh. 11.1 - Prob. 24ESCh. 11.1 - Prob. 25ESCh. 11.1 - Prob. 26ESCh. 11.1 - Prob. 27ESCh. 11.1 - Prob. 28ESCh. 11.2 - A sentence of the form Ag(n)f(n) for every na...Ch. 11.2 - Prob. 2TYCh. 11.2 - Prob. 3TYCh. 11.2 - When n1,n n2 and n2 n5__________.Ch. 11.2 - Prob. 5TYCh. 11.2 - Prob. 6TYCh. 11.2 - Prob. 1ESCh. 11.2 - Prob. 2ESCh. 11.2 - The following is a formal definition for ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - Prob. 6ESCh. 11.2 - Prob. 7ESCh. 11.2 - Prob. 8ESCh. 11.2 - Prob. 9ESCh. 11.2 - Prob. 10ESCh. 11.2 - Prob. 11ESCh. 11.2 - Prob. 12ESCh. 11.2 - Prob. 13ESCh. 11.2 - Use the definition of -notation to show that...Ch. 11.2 - Prob. 15ESCh. 11.2 - Prob. 16ESCh. 11.2 - Prob. 17ESCh. 11.2 - Prob. 18ESCh. 11.2 - Prob. 19ESCh. 11.2 - Prob. 20ESCh. 11.2 - Prove Theorem 11.2.4: If f is a real-valued...Ch. 11.2 - Prob. 22ESCh. 11.2 - Prob. 23ESCh. 11.2 - a. Use one of the methods of Example 11.2.4 to...Ch. 11.2 - Suppose P(n)=amnm+am1nm1++a2n2+a1n+a0 , where all...Ch. 11.2 - Prob. 26ESCh. 11.2 - Prob. 27ESCh. 11.2 - Prob. 28ESCh. 11.2 - Use the theorem on polynomial orders to prove each...Ch. 11.2 - Prob. 30ESCh. 11.2 - Prob. 31ESCh. 11.2 - Prob. 32ESCh. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prob. 34ESCh. 11.2 - Prob. 35ESCh. 11.2 - Prob. 36ESCh. 11.2 - Prob. 37ESCh. 11.2 - Prob. 38ESCh. 11.2 - Prob. 39ESCh. 11.2 - Prob. 40ESCh. 11.2 - Prob. 41ESCh. 11.2 - Prob. 42ESCh. 11.2 - Prob. 43ESCh. 11.2 - Prob. 44ESCh. 11.2 - Prob. 45ESCh. 11.2 - Prob. 46ESCh. 11.2 - Prob. 47ESCh. 11.2 - Prob. 48ESCh. 11.2 - Prob. 49ESCh. 11.2 - Prob. 50ESCh. 11.2 - Prob. 51ESCh. 11.3 - When an algorithm segment contains a nested...Ch. 11.3 - Prob. 2TYCh. 11.3 - Prob. 3TYCh. 11.3 - Suppose a computer takes 1 nanosecond ( =109...Ch. 11.3 - Prob. 2ESCh. 11.3 - Prob. 3ESCh. 11.3 - Exercises 4—5 explore the fact that for relatively...Ch. 11.3 - Prob. 5ESCh. 11.3 - Prob. 6ESCh. 11.3 - Prob. 7ESCh. 11.3 - Prob. 8ESCh. 11.3 - Prob. 9ESCh. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - Prob. 13ESCh. 11.3 - Prob. 14ESCh. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - Prob. 16ESCh. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - Prob. 18ESCh. 11.3 - Prob. 19ESCh. 11.3 - Prob. 20ESCh. 11.3 - Prob. 21ESCh. 11.3 - Construct a trace table showing the action of...Ch. 11.3 - Construct a trace table showing the action of...Ch. 11.3 - Prob. 24ESCh. 11.3 - Prob. 25ESCh. 11.3 - Prob. 26ESCh. 11.3 - Consider the recurrence relation that arose in...Ch. 11.3 - Prob. 28ESCh. 11.3 - Prob. 29ESCh. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Prob. 31ESCh. 11.3 - Prob. 32ESCh. 11.3 - Prob. 33ESCh. 11.3 - Prob. 34ESCh. 11.3 - Prob. 35ESCh. 11.3 - Prob. 36ESCh. 11.3 - Prob. 37ESCh. 11.3 - Prob. 38ESCh. 11.3 - Prob. 39ESCh. 11.3 - Prob. 40ESCh. 11.3 - Prob. 41ESCh. 11.3 - Exercises 40—43 refer to another algorithm, known...Ch. 11.3 - Prob. 43ESCh. 11.4 - The domain of any exponential function is , and...Ch. 11.4 - Prob. 2TYCh. 11.4 - Prob. 3TYCh. 11.4 - Prob. 4TYCh. 11.4 - Prob. 5TYCh. 11.4 - Graph each function defined in 1-8. 1. f(x)=3x for...Ch. 11.4 - Prob. 2ESCh. 11.4 - Prob. 3ESCh. 11.4 - Prob. 4ESCh. 11.4 - Prob. 5ESCh. 11.4 - Prob. 6ESCh. 11.4 - Prob. 7ESCh. 11.4 - Prob. 8ESCh. 11.4 - Prob. 9ESCh. 11.4 - Prob. 10ESCh. 11.4 - Prob. 11ESCh. 11.4 - Prob. 12ESCh. 11.4 - Prob. 13ESCh. 11.4 - Prob. 14ESCh. 11.4 - Prob. 15ESCh. 11.4 - Prob. 16ESCh. 11.4 - Prob. 17ESCh. 11.4 - Prob. 18ESCh. 11.4 - Prob. 19ESCh. 11.4 - Prob. 20ESCh. 11.4 - Prob. 21ESCh. 11.4 - Prob. 22ESCh. 11.4 - Prob. 23ESCh. 11.4 - Prob. 24ESCh. 11.4 - Prob. 25ESCh. 11.4 - Prob. 26ESCh. 11.4 - Prob. 27ESCh. 11.4 - Prob. 28ESCh. 11.4 - Prob. 29ESCh. 11.4 - Prob. 30ESCh. 11.4 - Prob. 31ESCh. 11.4 - Prob. 32ESCh. 11.4 - Prove each of the statements in 32—37, assuming n...Ch. 11.4 - Prob. 34ESCh. 11.4 - Prob. 35ESCh. 11.4 - Prob. 36ESCh. 11.4 - Prob. 37ESCh. 11.4 - Prob. 38ESCh. 11.4 - Prob. 39ESCh. 11.4 - Prob. 40ESCh. 11.4 - Show that log2n is (log2n) .Ch. 11.4 - Prob. 42ESCh. 11.4 - Prob. 43ESCh. 11.4 - Prob. 44ESCh. 11.4 - Prob. 45ESCh. 11.4 - Prob. 46ESCh. 11.4 - Prob. 47ESCh. 11.4 - Prob. 48ESCh. 11.4 - Prob. 49ESCh. 11.4 - Prob. 50ESCh. 11.4 - Prob. 51ESCh. 11.5 - Prob. 1TYCh. 11.5 - To search an array using the binary search...Ch. 11.5 - Prob. 3TYCh. 11.5 - Prob. 4TYCh. 11.5 - The worst-case order of the merge sort algorithm...Ch. 11.5 - Prob. 1ESCh. 11.5 - Prob. 2ESCh. 11.5 - Prob. 3ESCh. 11.5 - Prob. 4ESCh. 11.5 - In 5 and 6, trace the action of the binary search...Ch. 11.5 - Prob. 6ESCh. 11.5 - Prob. 7ESCh. 11.5 - Prob. 8ESCh. 11.5 - Prob. 9ESCh. 11.5 - Prob. 10ESCh. 11.5 - Prob. 11ESCh. 11.5 - Prob. 12ESCh. 11.5 - Prob. 13ESCh. 11.5 - Prob. 14ESCh. 11.5 - Prob. 15ESCh. 11.5 - Prob. 16ESCh. 11.5 - Trace the modified binary search algorithm for the...Ch. 11.5 - Prob. 18ESCh. 11.5 - Prob. 19ESCh. 11.5 - Prob. 20ESCh. 11.5 - Prob. 21ESCh. 11.5 - Prob. 22ESCh. 11.5 - Prob. 23ESCh. 11.5 - Show that given an array a[bot],a[bot+1],,a[top]of...Ch. 11.5 - Prob. 25ESCh. 11.5 - Prob. 26ES
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