Download Domain: Cluster: Level: Mathematical Content Standard: Featured

Domain:
Cluster:
Level:
Using Probability to Make Decisions S-MD
Calculate expected values and use them to solve problems
High School: Statistics*
Mathematical Content Standard:
1. (+) 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.
Featured Mathematical
Practice:
Pacing:
Graph a probability distribution.


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.
A2.6.F
Make sense of problems and
persevere in solving them.
Standard Clarification/Example:
Task Analysis:
Correlated WA Standard:
Vocabulary:
Prior

Sample space
Explicit


Random variable
Probability
distribution
Introductory
Sample Assessment Item:
Domain:
Cluster:
Level:
Using Probability to Make Decisions S-MD
Calculate expected values and use them to solve problems
High School: Statistics*
Mathematical Content Standard:
2. (+) Calculate the expected value of a random variable; interpret it as the
mean of the probability distribution.
Featured Mathematical
Practice:
Not currently an Algebra 2 standard
Make sense of problems and
persevere in solving them.
Standard Clarification/Example:
Pacing:
Calculate expected value of an event.
Task Analysis:


Correlated WA Standard:
Calculate the expected value of a random variable.
Interpret expected value as the mean of the probability distribution.
Vocabulary:
Prior


Mean
Probability
distribution
Explicit

Expected value
Introductory
Sample Assessment Item:
Domain:
Cluster:
Level:
Using Probability to Make Decisions S-MD
Calculate expected values and use them to solve problems
High School: Statistics*
Mathematical Content Standard:
3. (+) 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.
Featured Mathematical
Practice:
Not currently an Algebra 2 standard
Make sense of problems and
persevere in solving them.
Standard Clarification/Example:
Pacing:
Develop a probability distribution to find the expected value of an event.
Task Analysis:

Correlated WA Standard:
Develop a probability distribution for a random variable defined for
sample space in which theoretical probabilities can be calculated.
 Find the expected value for a probability distribution.
Vocabulary:
Prior



Random variable
Sample space
Probability
distribution
Explicit


Theoretical
probability
Expected value
Introductory
Sample Assessment Item:
Domain:
Cluster:
Level:
Using Probability to Make Decisions S-MD
Calculate expected values and use them to solve problems
High School: Statistics*
Mathematical Content Standard:
4. (+) 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?
Featured Mathematical
Practice:
Pacing:
Develop a probability distribution of a sample space.
Task Analysis:

Not currently an Algebra 2 standard
Make sense of problems and
persevere in solving them.
Standard Clarification/Example:

Correlated WA Standard:
Develop a probability distribution for a random variable defined for a
sample space in which probabilities are assigned empirically.
Find the expected value of a random variable for a probability
distribution.
Vocabulary:
Prior




Expected value
Random variable
Sample space
Probability
distribution
Explicit

Empirical
probability
Introductory
Sample Assessment Item:
Domain:
Cluster:
Level:
Using Probability to Make Decisions S-MD
Use probability to evaluate outcomes of decisions
High School: Statistics*
Mathematical Content Standard:
5. (+) Weigh the possible outcomes of a decision by assigning probabilities to
payoff values and finding expected values.
a. 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.
Featured Mathematical
Practice:
Not currently an Algebra 2 standard
Make sense of problems and
persevere in solving them.
Standard Clarification/Example:
Pacing:
Find the expected value for a game of chance.
Task Analysis:

Correlated WA Standard:
Weigh the possible outcomes of a decision by assigning probabilities to
payoff values.
 Find expected values for games of chance.
Vocabulary:
Prior



Expected value
Outcome
Payoff
Explicit
Introductory
Sample Assessment Item:
Domain:
Cluster:
Level:
Using Probability to Make Decisions S-MD
Use probability to evaluate outcomes of decisions
High School: Statistics*
Mathematical Content Standard:
5. (+) Weigh the possible outcomes of a decision by assigning probabilities to
payoff values and finding expected values.
b. 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.
Featured Mathematical
Practice:
Reason abstractly and
quantitatively.
Pacing:
Evaluate and compare the use of strategies based on the expected value of an event.


Evaluate the use of strategies on the basis of expected values.
Compare the use of strategies on the basis of expected values.
Not currently an Algebra 2 standard
Make sense of problems and
persevere in solving them.
Standard Clarification/Example:
Task Analysis:
Correlated WA Standard:
Vocabulary:
Prior


Payoff
Expected value
Explicit
Introductory
Sample Assessment Item:
Domain:
Cluster:
Level:
Using Probability to Make Decisions S-MD
Use probability to evaluate outcomes of decisions
High School: Statistics*
Mathematical Content Standard:
6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a
random number generator).
Featured Mathematical
Practice:
A2.6.A
Make sense of problems and
persevere in solving them.
Standard Clarification/Example:
Pacing:
Use a random number generator to simulate probability events.
Task Analysis:
 Use probabilities to make fair decisions by using random processes
such drawing by lots or using a random number generator.
Correlated WA Standard:
Vocabulary:
Prior
Explicit

Random number
generator
Introductory
Sample Assessment Item:
Domain:
Cluster:
Level:
Using Probability to Make Decisions S-MD
Use probability to evaluate outcomes of decisions
High School: Statistics*
Mathematical Content Standard:
7. (+) Analyze decisions and strategies using probability concepts (e.g.,
product testing, medical testing, pulling a hockey goalie at the end of a
game).
Featured Mathematical
Practice:
Pacing:
Analyze decisions and strategies using probability concepts.

Analyze decisions and strategies using probability concepts.
Not currently an Algebra 2 standard
Make sense of problems and
persevere in solving them.
Standard Clarification/Example:
Task Analysis:
Correlated WA Standard:
Vocabulary:
Prior
Explicit
Introductory
Sample Assessment Item: