### Probability and Statistics B

Semester B of Probability and Statistics is designed to give 11th- and 12th-grade students a more in-depth look at statistics and its many applications, with an emphasis on inferential statistics. Students are also introduced to advanced counting techniques as well as probability and its applications.

The semester begins with the concept of sample space, basic probability, and the difference between theoretical and experimental probabilities. A more in-depth look at probability follows, with an emphasis on compound and conditional probabilities.

Students explore normal data distributions and its properties, followed by a look at the standard normal distributions and its usefulness as a probability model for making inferences about a population. The remainder of the semester is devoted to hypothesis testing using various significance tests such as 1- and 2-sample z-tests, 1- and 2-sample t-tests, significance tests involving proportions, and chi-square goodness of fit tests. Hypothesis testing is then put into practice through a variety of real-world of applications and projects.

Each of the five units in Semester B includes twelve lessons and one project. Each lesson has a minimum of thirteen formativeassessment questions to enable students and their teacher to gauge student understanding. Summative assessments include three quizzes in each unit, a test for each unit, and a semester exam covering all five units. Each project uses concepts covered in the unit.

• Unit 1: Determine theoretical and experimental probabilities using probability rules and determine if two events are independent.
• Unit 2: Identify mutually exclusive and non-mutually exclusive events, determine binomial probabilities, and calculate expected value.
• Unit 3: Use permutations and combinations to calculate probabilities and apply the properties of normally distributed data.
• Unit 4: Understand the central limit theorem, determine confidence intervals, and use hypothesis testing to compare proportions and means, and to determine the relationship between categorical variables.
• Unit 5: Distinguish between parametric and non-parametric statistics and apply these concepts to examine topics including health science and market research.

State: National
Grade Level: 9, 10, 11, 12
Category: Math
Course Length: Semester