Download Unit 4

Department: Mathematics
Understanding by Design
Course: AP Statistics
Unit 4 - Probability (Chapter 6 - 9)
Standard(s):
S-CP.2 Understand independence and conditional probability and use them to interpret data. Understand that two events
A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this
characterization to determine if they are independent.
S-CP.3 Understand independence and conditional probability and use them to interpret data. Understand the conditional
probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional
probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as
the probability of B.
S-CP.4 Understand independence and conditional probability and use them to interpret data. Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the two-way table
as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect
data from a random sample of students in your school on their favorite subject among math, science, and English.
Estimate the probability that a randomly selected student from your school will favor science given that the student is in
tenth grade. Do the same for other subjects and compare the results.
S-CP.5 Understand independence and conditional probability and use them to interpret data. Recognize and explain the
concepts of conditional probability and independence in everyday language and everyday situations. For example,
compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
S-CP.6 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Find the
conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in
terms of the model.
S-CP.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply
the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
S-CP.8 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Apply
the general Multiplication Rule in a uniform probability model, P(A and B) = [P(A)]x[P(B|A)] =[P(B)]x[P(A|B)], and
interpret the answer in terms of the model.
S-CP.9 Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use
permutations and combinations to compute probabilities of compound events and solve problems.
S-MD.1 Calculate expected values and use them to solve problems. Define a random variable for a quantity of interest by
assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the
same graphical displays as for data distributions.
S-MD.2 Calculate expected values and use them to solve problems. Calculate the expected value of a random variable;
interpret it as the mean of the probability distribution.
S-MD.3 Calculate expected values and use them to solve problems. Develop a probability distribution for a random
variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For
example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five
questions of a multiple-choice test where each question has four choices, and find the expected grade under various
grading schemes.
S-MD.4 Calculate expected values and use them to solve problems. Develop a probability distribution for a random
variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example,
find a current data distribution on the number of TV sets per household in the United States, and calculate the expected
number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
S-MD.5 Use probability to evaluate outcomes of decisions. Weigh the possible outcomes of a decision by assigning
probabilities to payoff values and finding expected values.
S-MD.5a Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery
ticket or a game at a fast-food restaurant.
S-MD.5b Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible
versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major
accident.
S-MD.6 Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions (e.g., drawing by lots,
using a random number generator).
S-MD.7 Use probability to evaluate outcomes of decisions. Analyze decisions and strategies using probability concepts
(e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Stage 1: Desired Results
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Understandings
Certain outcomes happen with a definite chance of happening; this is called probability. Different types of events can
lead to different outcomes, therefore their probabilities (as well as their collection of probabilities) may be different.
•Random variables can be used to model real-life situations to help find the probability of events happening
•Situations with only two outcomes can be modeled using variables that can be defined to act binomially or geometrically
•When wanting to estimate something about a population, we can take samples and study their behavior
Essential Questions
Knowledge & Skill
How is the probability of an outcome determined?
•Why are there different probability models for different
situations?
•How do different samples behave? And how can we use
that knowledge of their behavior to estimate things about
the population?
Unit Objectives (I can)
Section 9.1
Differentiate between a parameter and a statistic
Understand what a sampling distribution is
escribe a sampling distribution center, spread,
shape for both p s and s
Understand the bias and variability of a statistic
and what they do to the sampling distribution
Section 9.2
escribe the sampling distribution for p s
Prove the above using rule of thumb I and II
Use the normal approximation to solve problems
AN I’VE REVIEWE CHAPTER 2!
Section 9.3
escribe the sampling distribution for s
Prove the above
Understand the central limit theorem and how it
relates to the distribution of the above
Use the normal approximation to solve problems
AN I’VE REVIEWE CHAPTER 2!
Section 6.1
Understand the concept of random behavior
Understand what makes a trial independent
Section 6.2
Identify and list a sample space
Use tree diagrams to identify above, and the
multiplication rule to find the total number of outcomes
Differentiate between samples with replacement and
without replacement, and understand how that affects
finding a probability
List and apply the probability rules to find the probability
of events
Apply the multiplication rule for independent events
Section 6.3
Apply the addition rule to find the union of events
Apply the general multiplication rule (not just for
independent events)
Recognize events requiring the conditional probability rule
Identify the difference between events that are disjoint
and not
Differentiate between the number of trials and the number
of repetitions
Section 7.1
Identify a random variable
Differentiate between discrete and continuous random
variables
Determine whether a probability distribution is legitimate
Find probabilities of outcomes of both kinds of random
variables
ifferentiate between ≤ and < in discrete and continuous
random variables
Calculate and create the probability distribution of a
random variable
Section 7.2
Calculate the means and variances of random variables
Understand the law of large numbers and how it relates to
Stage 2: Assessment Evidence
Test, quizzes, homework, worksheets, in-class activities.
Performance Task Summary
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Worksheets
Homework
Quizzes
Tests
Activities to be done at the teachers discretion:
Summary/Exit Slips
various book problems
worksheets
Casino Lab
Estimating Probabilities activity
Self-Assessments
Rubric Titles
Assessments will contain free response, mutliple choice,
and matching sections as well.
Other Evidence, Summarized
Self Evaluation of skills on "Objectives" sheet.
Stage 3: Learning Activities
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Students will perform daily activites (notes, classwork, homework, etc) to demonstrate their understanding of the learning
targets. Students will be assessed on their understanding of the vocabulary and be able to summarize the days materials.
Students will be provided with frequent feedback during daily lessons, homework, quizzes, and the unit test.
Some activites that can be used are as follows:
Summary/Exit Slips
various book problems
worksheets
Casino Lab
Estimating Probabilities activity