Bronx Community College of the City University of New York

Department of Mathematics and Computer Science

 

Syllabus:  MTH 23 Probability and Statistics (3 credits, 3 hours per week)

 

Prerequisite:  MTH 5 or equivalent; co-requisite ENG 2 and/or RDL 2 if required

 

TEXT (Bundle):  Understanding Basic Statistics by Brase & Brase, Loose-leaf version, 7th ed. + MindTap Statistics, 1 term (6 months) Instant Access, Cengage Learning.   (7th Edition, ISBN-10: 1337349097, ISBN-13: 9781337349093)

 

Calculator: scientific calculator (suggested: TI-36X Pro)

Learning Objectives: On successful completion of this course, students will be able to

  1. Sort, analyze and present numerical data using sample spaces, measures of central tendency, measures of variation, and measures of dispersion.
  2. 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.
  3. Predict experimental outcomes using basic techniques of probability (permutations, combinations, counting techniques, tree diagrams).
  4. Recognize the features of a binomial experiment and apply the binomial probability distribution.
  5. Recognize the features of a normal distribution and compute probabilities using the standard normal distribution.
  6. Infer population parameters using sampling distributions and the Central Limit Theorem.
  7. Limit the error of estimation by calculating confidence intervals.
  8. Accept or reject a hypothesis by establishing a level of significance.

 

This course addresses the following General Education Proficiencies: analysis, interpretation, evaluation, and integration of information to formulate and solve problems; use of mathematical and scientific methods to formulate and solve problems and to understand the physical, natural and social worlds.  This course may be used to satisfy Category A (Mathematical and Quantitative Reasoning) of the CUNY Pathways Required Core.

 

Topics, Text Sections and Homework: (*optional topics)

 

 

SECTION

TOPIC

PAGES

PROBLEMS

1. Getting Started

1.1

What is statistics?

10-12

1-15

1.2

Random Samples

18-20

1-3, 8-20

 

1.3

Introduction to Experimental Design

29-31

1, 2, 5-11

2. Organizing Data

2.1

Frequency Distributions, Histograms, and Related Topics

52-59

1-10, 15-20

2.2*  

Bar Graphs, Circle Graphs, and Time-Series Graphs

65-69

1-14

2.3*

Stem-and-Leaf Displays

73-76

1-9

3. Averages and Variation

3.1

Measures of Central Tendency: Mode, Median, and Mean

95-99

1, 2, 5-7, 12-28

3.2

Measures of Variation

111-114

1-21

3.3

Percentiles and

Box-and-Whisker Plots*

127-128

1-11

4. Correlation and Regression

4.1

Scatter Diagrams and Linear Correlation

154-157

1-18

4.2*

Linear Regression and the Coefficient of Determination

171-175

1-18

5. Elementary Probability Theory

5.1

What is Probability?

198-200

1-4, 7-20

5.2

Some Probability Rules– Compound Events

215-220

1-8, 11-31

5.3*

Trees and Counting Techniques

229-231

1-27

6. The Binomial Probability Distribution

     and Related Topics

6.1

Introduction to Random Variables and Probability Distributions

248-252

1-3, 6-18

6.2

Binomial Probabilities

264-269

1-27

6.3

Additional Properties of the Binomial Distribution

274-278

1-8, 11-22

7. Normal Curves and Sampling Distributions

7.1

Graphs of Normal Probability Distribution

297-299

1-11

7.2

Standard Units and Areas Under the Standard Normal Distribution

309-311

1-50

7.3

Areas Under any Normal Curve

321-324

1-30

7.4

Sampling Distributions

331

1-9

7.5

The Central Limit Theorem

339-343

1-20

7.6

Normal Approximation to the Binomial Distribution

350-353

1-21

8. Estimation

8.1

Estimating μ when σ is Known

377-382

1-25

8.2

Estimating μ when σ is Unknown

390-395

1-22

8.3*

Estimating p in the Binomial Distribution

403-407

1-27

9. Hypothesis Testing

9.1

Introduction to Statistical Tests

432-436

1-24

9.2

Testing the Mean μ

447-451

1-24

9.3*

Testing a Proportion p

458-463

1-24

 

Suggested Grading Guidelines: Homework, quizzes, oral presentations, projects, etc. (1/3 of grade); In-class tests (1/3 of grade); Final Exam (1/3 of grade).

 

SLF 4/09 AW 3/10 RG 5/12 KD 3/15 KD 8/16