Reference no: EM132585279
1. Apply the order of operations to solve discipline-specific problems involving probabilities and counting principles.
2. Calculate applications of mathematical problems involving probabilities.
3. Differentiate between the concepts of odds and probabilities, as well as permutations and combinations, and identify how they relate to one another.
4. Identify and choose viable likelihoods based on calculated probabilities.
Logic and Decision Making
A proposed directed study MATH125 class comprising 25 students earned the following grades on the first unit:
|
MATH125
|
Total
|
Percentage
|
Unit 1
|
U1DB2
|
U1DB
|
U1i
|
U1SA
|
|
Class
|
Letter
|
Grade
|
Points
|
Points
|
Points
|
Points
|
Points
|
|
Names
|
Grade
|
Total (100)
|
Total (200)
|
Total (50)
|
Total (10)
|
Total (50)
|
Total (90)
|
|
Student #1
|
B-
|
82%
|
163
|
48
|
10
|
50
|
55
|
|
Student #2
|
C-
|
72%
|
144
|
34
|
0
|
40
|
70
|
|
Student #3
|
C
|
74%
|
148
|
40
|
10
|
43
|
55
|
|
Student #4
|
A
|
93%
|
186
|
50
|
10
|
36
|
90
|
|
Student #5
|
B+
|
87%
|
174
|
48
|
10
|
46
|
70
|
|
Student #6
|
F
|
56%
|
112
|
44
|
5
|
28
|
35
|
|
Student #7
|
B
|
84%
|
168
|
50
|
10
|
43
|
65
|
|
Student #8
|
B-
|
80%
|
159
|
46
|
10
|
48
|
55
|
|
Student #9
|
C+
|
79%
|
158
|
50
|
10
|
73
|
25
|
|
Student #10
|
B
|
86%
|
172
|
33
|
5
|
44
|
90
|
|
Student #11
|
B-
|
80%
|
159
|
34
|
10
|
50
|
65
|
|
Student #12
|
C+
|
77%
|
154
|
40
|
5
|
44
|
65
|
|
Student #13
|
A-
|
90%
|
179
|
36
|
10
|
43
|
90
|
|
Student #14
|
C
|
73%
|
145
|
42
|
10
|
38
|
55
|
|
Student #15
|
D
|
66%
|
131
|
28
|
0
|
33
|
70
|
|
Student #16
|
B+
|
87%
|
174
|
34
|
10
|
50
|
80
|
|
Student #17
|
C+
|
79%
|
158
|
30
|
0
|
43
|
85
|
|
Student #18
|
B-
|
80%
|
159
|
46
|
10
|
38
|
65
|
|
Student #19
|
C+
|
78%
|
155
|
22
|
10
|
33
|
90
|
|
Student #20
|
D
|
61%
|
121
|
28
|
10
|
38
|
45
|
|
Student #21
|
B-
|
80%
|
159
|
34
|
10
|
50
|
65
|
|
Student #22
|
B+
|
88%
|
175
|
40
|
10
|
50
|
75
|
|
Student #23
|
B
|
85%
|
169
|
41
|
0
|
43
|
85
|
|
Student #24
|
B-
|
80%
|
160
|
22
|
10
|
48
|
80
|
|
Student #25
|
C
|
74%
|
148
|
50
|
10
|
33
|
55
|
1. Calculate the class average for Unit 1. Using the "Grading Scale"listed below with the "Percentage Grade Total"above,what is the overall class average "Letter Grade"?
|
Grading Scale
|
|
|
|
Letter Grade
|
Percentage
|
Letter Grade
|
Percentage
|
|
A
|
93-100
|
C+
|
77-79.99
|
|
A-
|
90-92.99
|
C
|
73-76.99
|
|
B+
|
87-89.99
|
C-
|
70-72.99
|
|
B
|
83-86.99
|
D+
|
67-69.99
|
|
B-
|
80-82.99
|
D
|
60-66.99
|
To find the class average you add unit point totals altogether and divide by 25 the total number of students.
2. Create a frequency table to show the distribution of grades across the grading scale for the first week.
3. Describe what you see based on the frequency distribution.
4. Calculate the mean, median, and mode for the class's first unit "Percentage Grade Total" grades.
5. Use the formulas for range, population variance, and population standard deviation with the"Percentage GradeTotal" to complete the following table. Make sure to check your answers with MS Excel. Also, round your answers to four decimal values.
6. At AIU, the following hypothetical propositions, p and q,are typically found to be true:
p: I redo my previous unit's intellipath nodes.
q: I improve myoverall score.
Write out the conditional statement as a symbolic sentence.
Are these two symbolic sentences logically equivalent? Why, or why not?
7. The following hypothetical propositions, p and q, pertain strictly to Student #12 only.
p: They score 70 points on the Unit 5 Submission Assignment.
q: They will earn an 80% grade in the class.
Write out the conditional statement p → q as an English sentence.
Write out the conditional statement q → p as an English sentence.
Are these two English sentences logically equivalent? Why, or why not?
8. Fill out the following truth table to determine the possible outcomes for the compound statement ~q∨p.(15 points)
Is this compound statement a tautology (T), fallacy (F), or neither?