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, 7th ed. (Enhanced WebAssign access card & loose-leaf textbook), Cengage Learning.

(7th Edition, ISBN-13: 9781337372763, ISBN-10: 1337372765)

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 B (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