Apply the order of operations to solve discipline-specific problems involving probabilities and counting principles.

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Apply the order of operations to solve discipline-specific problems involving probabilities and counting principles.

MATH125: Unit 6 Submission Assignment Answer Form

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
ALL questions below must be answered. Show ALL step-by-step calculations, round all your final answers correctly, and include the units of measurement. Upload this modified Answer Form to the intellipath Unit 6 Submission lesson. Make sure that you submit your work in a modified MS Word document; handwritten work will not be accepted. If you need assistance, please contact your course instructor.
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

Class Average
Letter Grade

Unit 1
?
?

Show your work here: (5 points)
2. Create a frequency table to show the distribution of grades across the grading scale for the first week. (5 points)

Letter Grade
Percentage
Frequency #
Cumulative Frequency #

A
93–100
?
?

A-
90–92.9
?
?

B+
87–89.9
?
?

B
83–86.9
?
?

B-
80–82.9
?
?

C+
77–79.9
?
?

C
73–76.9
?
?

C-
70–72.9
?
?

D+
67–69.9
?
?

D
60–66.9
?
?

F
Below 59.9
?
?

3. Describe what you see based on the frequency distribution. (5 points)
4. Calculate the mean, median, and mode for the class’s first unit “Percentage Grade Total” grades.

Answers
(Rounded to the nearest percent)

Mean
?

Median
?

Mode
?

Show your work here: (15 points)
5. Use the formulas for range, population variance, and population standard deviation with the “Percentage Grade Total” to complete the following table. Make sure to check your answers with MS Excel. Also, round your answers to four decimal values.

Answers

Range
?

Variance
?

Standard deviation
?

Show your work here: (15 points)
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 my overall score.
Write out the conditional statement as a symbolic sentence.

English Sentence
Symbolic Sentence

If I redo my previous unit’s Intellipath nodes, then I improve my overall score.
?

Write out the conditional statement as a symbolic sentence.

English Sentence
Symbolic Sentence

If my overall score did not improve, then I did not redo my previous unit’s intellipath nodes.
?

Are these two symbolic sentences logically equivalent? Why, or why not? (15 points)
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.

Symbolic Sentence
English Sentence

p → q
?

Write out the conditional statement q → p as an English sentence.

Symbolic Sentence
English Sentence

q → p
?

Are these two English sentences logically equivalent? Why, or why not? (15 points)
8. Fill out the following truth table to determine the possible outcomes for the compound statement ~ q ∨ p. (15 points)

p
q
~ q
~ q ∨ p

T
T
?
?

T
F
?
?

F
T
?
?

F
F
?
?

Is this compound statement a tautology (T), fallacy (F), or neither?

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