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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: