AP STATISTICS

UNIT 3: Probability Theory

High School Mathematics

The Practice of Statistics, 2nd Ed.

Target Time Frame: 11 – 14 days

STANDARD / ESSENTIAL QUESTION / DEPTH for MASTERY / Sections / COMMENTS
IIIA: Understand and apply the “Law of Large Numbers”, the addition and multiplication probability rules; find conditional probability; understand discrete random variables and their probability distributions, including binomial; conduct simulations of distributions, including binomial and geometric; compute the mean and standard deviation of a random variable; conduct transformation of a random variable. / What is the Law of Large Numbers?
When would I ever use probability?
How do I find the expected value of a discrete random variable?
What does Craps have to do with statistics?
What is the difference between a binomial distribution and a geometric one? / All / Ch. 5.3
Ch. 6.1, 6.3
Ch. 7.1, 7.2
Chapter 8 / Resources:
The Game of Craps (Activity 7, TPOS)
The Casino Lab (GRB)
Activity 8A-Plinko (GRB)
Special Problem 7A
Special Problem 6C (GRB)
2001-FR#2
IIIB: Understand the difference between independent and dependent variables and independent and disjoint; find the mean and standard deviation for sums and differences of independent random variables. / What is the difference between independent and dependent variables?
What does disjoint mean?
If two random variables are normal/not normal, how does that affect their linear combination? / All / Ch. 6.2
Ch. 7.2 / Resources:
2002-FR#3
2003B-FR#2
IIIC: Know properties of the normal distribution; use tables of the normal distribution; use the normal distribution as a model for measurements. / What is a z-score?
How do normal distributions relate to probability distributions? / All / Ch. 2.1, 2.2
Ch. 7.1 / Resources:
APEX-Classtools Online
IIID: Identify and calculate statistics to describe sampling distributions of sample proportions and sample means, and distributions of the difference between 2 sample proportions and 2 sample means; apply the Central Limit Theorem; simulate a sampling distribution. / What does it mean to have high variability of a statistic?
Can I use normal approximations?
What is the CLT?
How do I use my calculator or computer to conduct a simulation? / All / Ch. 5.3
Chapter 9 / Resources:
Activity 9A (TPOS)
1998-FR#1

UNIT COMMENTS: This unit must be completed prior to the AP Exam. Notes in the Comments column that have a year and FR# refer to an AP Exam, noting the year and free response question number.