BRONX COMMUNITY COLLEGE

 of the City University of New York

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

 

SYLLABUS

 

MTH 23.5: PROBABILITY AND STATISTICS WITH ALGEBRA (3 credits / 5 hours)

Prerequisite:    None. Students with Math Proficiency Index less than 40 are strongly encouraged to enroll in Math Start or CUNY Start, before taking college-level mathematics courses.

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: This course is appropriate for non-STEM majors with Math Proficiency Index below 40 who would benefit from a review of elementary algebra topics. This course covers the curriculum of a 3 credit probability and statistics course (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     EA 6/21