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UNIT 1: The Normal Distribution
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Pacing: 3 weeks
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Stage 1 Desired Results
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Established Goals:
- ID.A.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
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Transfer
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Students will be able to independently use their learning to….
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Apply the principles of normal distribution to recognize and analyze distributions in various contexts.
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Apply the concepts of z-scores, probability, and standard deviation to solve problems and make decisions in diverse scenarios.
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Utilize technology to analyze data sets, visualize distributions and draw conclusions about normality.
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Meaning
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Understandings
Students will understand…
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The standard deviation measures variability and spread in a normal distribution.
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How and when to apply the normal distribution model to solve practical problems and make informed decisions.
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The normal distribution curve is a family of symmetrical curves defined by the mean and the standard deviation.
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Areas under the curve represent probabilities associated with continuous distributions.
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The area under the curve is always to the left of the corresponding z-score.
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The distribution of outcomes of many real life events can be approximated by the normal curve.
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Essential Questions
Students will keep considering…
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What are the properties of a normal probability distribution?
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What are the key characteristics of a normal distribution? How can you recognize a normal distribution?
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How is the z-score used to standardize and compare values within a normal distribution?
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How does the standard deviation and mean affect the graph of the normal distribution?
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Acquisition
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Students will know…
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The characteristics of a normal distribution, including the bell-shaped curve, symmetry, and the empirical rule.
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How the standard deviation influences the shape and spread of a normal distribution.
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The concept of z-scores and their use in understanding and comparing values within a normal curve.
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The total area under the normal curve is 1.
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Part of the area under a normal curve represents the probability for a specific observation.
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Students will be skilled at…
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Calculating probabilities using z-tables or statistical software and interpreting the results in the context of the problem.
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Standardizing data using z-scores and interpreting the standardized values in practical terms.
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Creating and interpreting graphs (histograms, box plots) to visually represent normal distributions.
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