BRONX COMMUNITY COLLEGE
of the City University of New
York
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE
SYLLABUS
MTH 20: PROBABILITY AND STATISTICS WITH ALGEBRA (3 credits / 7 hours)
Prerequisite: MTH 1 or placement into MTH 5 or a proficiency index indicating a light developmental need as defined by CUNY (proficiency index between 40 and 59)
Co-requisite: ENG 2 and/or RDL 2, if required
Textbooks: 1. Brase & Brase, Understanding Basic Statistics, 8th ed., Cengage Learning
ISBN: 9781337558075
2. A. McInerney, MTH 5 Lecture Notes available at https://fsw01.bcc.cuny.edu/mathdepartment/Courses/Math/MTH05/05text0916b-hyper.pdf
Calculator: Scientific calculator (suggested: TI-36X Pro)
Course Description: This is a probability and statistics course
with elementary algebra topics integrated to support the statistics. Probability and statistics topics include
organization and presentation of data, measures of central tendency and
variation, correlation and linear regression, elementary probability, the
binomial and normal distributions, sampling distributions, the central limit
theorem, confidence intervals, student’s t-distribution, and hypothesis
tests. Elementary algebra topics include
fractions, percent, adding and subtracting polynomials, linear and quadratic
equations, literal equations, solving word problems, inequalities, and
functions.
Purpose: To reduce to one semester the sequence of courses leading
to a credit-bearing math course for non-STEM majors. This course covers the
curriculum of a 3 credit probability and statistics
course (presently offered as MTH 23) with supplemental instruction in elementary
algebra integrated on a “just in time” basis to support the probability and
statistics. This course is equivalent to
MTH 23 for grade replacement purposes. This course is not for STEM or Business
Administration AS majors and is not a prerequisite for any higher
level mathematics course. In
particular, this course does not
satisfy the prerequisites for MTH 6.
Student Learning Objectives: Upon completion of this course, students will be able to:
1. Perform operations with signed numbers using a calculator. Solve and graph linear equations. Solve literal equations and linear inequalities. Evaluate algebraic expressions and solve word problems. Evaluate functions and graph linear functions.
2. Sort, analyze and present numerical data using sample spaces, measures of central tendency, and measures of variation.
3. Recognize correlations between data sets using scatter diagrams; express linear correlations using least squares regression; determine the strength of the correlation via the correlation coefficient.
4. Predict experimental outcomes using basic techniques of probability (permutations, combinations, counting techniques, tree diagrams).
5. Recognize the features of a binomial experiment and apply the binomial probability distribution.
6. Recognize the features of a normal distribution and compute probabilities using the standard normal distribution.
7. Infer population parameters using sampling distributions and the Central Limit Theorem.
8. Limit the error of estimation by calculating confidence intervals.
9. Accept or reject a hypothesis by establishing a level of significance.
Pathways: This course may be used to satisfy Category B (Mathematical and Quantitative Reasoning) of the CUNY Pathways Required Core.
Grading Guidelines: Homework, quizzes, oral presentations, projects, etc. (1/3 of grade); midterm and in-class tests (1/3 of grade); final exam (1/3 of grade).
Academic
Integrity: Academic dishonesty (such as plagiarism and cheating) is
prohibited at Bronx Community College and is punishable by penalties, including
failing grades, dismissal and expulsion. For additional information and the
full policy on Academic Integrity, please consult the BCC College Catalog.
Accommodations/Disabilities:
Bronx Community College respects and welcomes students of all backgrounds
and abilities. In the event you encounter any barrier(s) to full participation
in this course due to the impact of a disability, please contact the disAbility Services Office as soon as possible this
semester. The disAbility Services
specialists will meet with you to discuss the barriers you are experiencing and
explain the eligibility process for establishing academic accommodations for
this course. You can reach the disAbility Services
Office at: disability.services@bcc.cuny.edu, Loew Hall, Room 211, (718) 289-5874.
Topics in Probability
and Statistics with Algebra: Section numbers preceding topics refer to Brase & Brase (for
probability and statistics) and McInerney (for elementary
algebra).
(* indicates optional topics; leave some
out as needed in order to do tests and review)
PROBABILITY AND
STATISTICS |
ELEMENTARY ALGEBRA |
|
Week 1 |
1.1 What is statistics? |
1, 2, 3.1 Review: arithmetic
of signed numbers, fractions, decimals, percent, rounding, and order of operations |
1.2 Random Samples |
Calculators: Arithmetic
and order of operations |
|
Week 2 |
1.3 Introduction to
Experimental Design 2.1 Frequency
Distributions, Histograms, and Related Topics |
3.2, 3.3, 3.4 Evaluating
algebraic expressions and translating algebraic expressions Supplement: Area of a
rectangle |
Week 3 |
2.2 Bar Graphs, Circle
Graphs, and Time-Series Graphs* 2.3 Stem-and-Leaf
Displays* 3.1 Measures of Central
Tendency: Mode, Median, and Mean |
8.2 Radicals Calculators: Descriptive
statistics |
Week 4 |
3.2 Measures of Variation |
6.2 Combining like terms,
adding and subtracting polynomials |
3.3 Percentiles and Box-and-Whisker Plots* |
4.1, 4.2,
4.3 Solving linear equations and applications to word problems |
|
Week 5 |
4.1 Scatter Diagrams and
Linear Correlation |
5.1, 5.2 Co-ordinate
system, graphs of linear equations, slope of a straight line, equation of a
line |
4.2 Linear Regression and
the Coefficient of Determination* |
|
|
Week 6 |
5.1 What is Probability? |
|
5.2 Some Probability
Rules– Compound Events Midterm Review |
4.3 Solving literal equations |
|
Week 7 |
Midterm 5.3 Trees and Counting
Techniques* |
6.3 Exponents and
properties |
6.1 Introduction to
Random Variables and Probability Distributions |
3.3 Functions and their
graphs |
|
Week 8 |
6.2 Binomial
Probabilities |
|
6.3 Additional Properties
of the Binomial Distribution |
||
Week 9 |
7.1 Graphs of Normal
Probability Distribution |
4.4 Inequalities and
interval notation, graphing linear inequalities on a number line |
7.2 Standard Units and
Areas Under the Standard Normal Distribution |
Supplement: Area under
the graph of a function, basic properties of area |
|
Week 10 |
7.3 Areas Under any
Normal Curve 7.4 Sampling Distributions |
|
Week 11 |
7.5 The Central Limit
Theorem |
|
7.6 Normal Approximation
to the Binomial Distribution |
|
|
Week 12 |
8.1 Estimating μ
when σ is Known |
4.4 Solving linear
inequalities |
8.2 Estimating μ
when σ is Unknown |
|
|
Week 13 |
8.3 Estimating p
in the Binomial Distribution* |
9.3,
9.4, 9.5 Solving quadratic equations by basic factoring and quadratic
formula, with applications to more advanced word problems |
9.1 Introduction to
Statistical Tests 9.2 Testing the Mean µ |
|
|
Week 14 |
9.3
Testing a Proportion p* |
|
Final Review |
|
RG/KO 10/19