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Logic and Decision-Making Case Essay

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Description/Paper InstructionsLogic and Decision-Making Case Essay

NAME:Lori Hackenburg 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

- 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)

- 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 ? ?

- Describe what you see based on the frequency distribution. (5 points)
- 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)

- 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)

- At AIU, the following hypothetical propositions, pand 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)

- The following hypothetical propositions, pand 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)

- 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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