Math Homework

NAME:

MATH125: Unit 6 Individual Project 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 Unit 6 Individual Project. 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	U1IP
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 Indvidual Project.

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?