AP STATISTICS: Ms. Jetmore 2015-2016
Syllabus Chapter 6: Random Variables
Day Topic
T Nov 10 Chapter 6 Introduction, Sec 6.1 – Discrete
Random Variables, Mean (Expected Value) of a Discrete Random Variable
Homework p. 353; 1, 5, 7, 9, 13
Read 346-353
W Nov 11 Sec 6.1 – Standard Deviation (and Variance) of a Discrete Random Variable, Continuous p. 354; 15, 19, 23, 25, 27-30
Read 358-363
Random Variables
R Nov 12 Sec 6.2 – Linear Transformations
F Nov 13 Sec 6.2 – Combining Random Variables,
Combining Normal Random Variables p. 378; 37, 39-41, 43, 45
Read 364-377 p. 379; 49, 51, 57-59, 63, 65, 66
Review 340-377
SATURDAY NOVEMBER 14
TH
AP STUDENT CONFERENCE AT RICHMOND HIGH SCHOOL
M Nov 16 Review Sec 6.1 and 6.2 – AP multiple choice
Quiz 6.1 and 6.2
T Nov 17 Sec 6.3 – Binomial Settings and Binomial
Random Variables, Binomial Probabilities
Read 382-389 p. 403; 69, 71, 73, 75, 77
Read 390-397
W Nov 18 Sec 6.3 – Mean and Standard Deviation of a
Binomial Distribution, Binomial Distributions in Statistical Sampling
R Nov 19 Sec 6.3 – Geometric Random Variables
F Nov 20 Chapter 6 Review p. 404; 79, 81, 83, 85, 87, 89
Read 397-403 p. 405; 93, 95, 97, 99, 101-103
Review 340-403
Ch Review p. 408; 1-8
M Nov 23 Chapter 6 Review
T Nov 24 Chapter 6 TEST
Ch Test (optional) p. 409; 1-14
Tutoring is available most mornings 7:30-8:00am and after school Wednesday 3:45-4:30

Chapter Objectives
Section 6.1 – Discrete and Continuous Random Variables

Use a probability distribution to answer questions about possible values of a random variable.

Calculate the mean and standard deviation of a discrete random variable.

Interpret the mean and standard deviation of a random variable.
Section 6.2 – Transforming and Combining Random Variables

Describe the effects of transforming a random variable by adding or subtracting a constant and multiplying or dividing by a constant.

Find the mean and standard deviation of the sum or difference of independent random variables.

Determine whether two random variables are independent.

Find probabilities involving the sum or difference of independent Normal random variables.
Section 6.3 – Binomial and Geometric Random Variables

Determine whether the conditions for a binomial random variable are met.

Calculate the mean and standard deviation of a binomial random variable. Interpret these values in context.

Compute and interpret probabilities involving binomial distributions.

Find probabilities involving geometric random variables.

Determine whether the conditions for the Normal approximation to a binomial distribution are met.
When appropriate, use the Normal approximation to estimate probabilities in a binomial setting.
AP Exam Tips

If the mean of a random variable has a non-integer value, but you report it as an integer, your answer will be marked as incorrect.

When you solve problems involving random variables, start by defining the random variable of interest.
For example, let x = the Apgar score of a randomly selected baby or let y = the height of a randomly selected young woman. Then state the probability you’re trying to find in terms of the random variable:
P( 68

Y

70) or P( X

7)

If you have trouble solving problems involving sums and differences of Normal random variables with the algebraic methods shown earlier in the section, use the simulation strategy from the Technology
Corner to earn some (or possibly full) credit.

2005B
2006B
2008
2008B
2010
2010B
1999
1999
2001
2002
2002B
2003
2004
2004
2005
Free-Response Questions from Previous AP Exams
Questions can be found on the AP Central Web site: http://apcentral.collegeboard.com/apc/members/exam/exam_questions/8357.html.
Students should be able to answer all the free-response questions listed with material in this chapter. Questions that contain content from this chapter but also require content from later chapters are listed in the last chapter required to complete the entire question. Some of these problems we will do in class as warm-up problems.
You may do the others to help you understand the content from this chapter as well as to prepare for the AP exam in May.
Year Question Content
1998 6 Normal calculations, simulation, expected value
3
2
3
3
4
2
4
5
2
Normal calculations, binomial calculations, outlier rules
Sample space, expected value
Expected value
Normal calculations, combining independent random variables
Addition rule, expected value, conditional probability
Normal calculations, binomial calculations
Binomial conditions, multiplication rule, interpreting probability, generalizability
Conditional probability, expected value
Expected value, median of a discrete random variable, relationship of mean
2
3
3
5
4
3 and medial
Mean and standard deviation of a discrete random variable, combining independent random variables, linear transformations of a random variable
Normal calculations, binomial calculations, inverse Normal calculations
Expected value, basic probability rules
Combining Normal random variables, Normal calculations
Mean and standard deviation of a binomial distribution, binomial calculations, stratified sampling
Binomial distribution, expected value, binomial calculations