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

# 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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