Alliance for Catholic Education (ACE)Notre Dame, Indiana, US,

November 1, 2008

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Unit cover page for Normal Distributions unit.

- Mathematics > General
- Mathematics > Data Analysis & Probability
- Mathematics > Statistics

- Grade 11
- Grade 12

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Probability & Statistics-College Prep (Grade 12)

**Unit Number:**

6

**Estimated Duration:**19 days

**Unit Rationale:**The second semester of Prob/Stats focuses on probability distributions and inferential statistics, so it is natural that it begins with the normal probability distribution. This is the most common distribution curve and the distribution that is often familiar to students under the 'bell-curve' title. The students are prompted to ask and answer questions like "What are the characteristics of a normal curve?", "Given a normal distribution, how are probabilities/areas calculated?", "Do normal curves appear in real-world data?" [yes!]. This unit establishes the basis for the next unit on the Central Limit Theorem (which demonstrates the true power and versatility of the normal distribution curve). The skills used to analyze the normal distribution in this unit could also be extended in a future stats class to other types of distributions. (Understanding Basic Statistics, 3e, Brase&Brase: Ch. 7.1, 7.2, 7.3)

**Unit Goal:**SWBAT analyze normal and standardized normal distributions.

**Prior Knowledge:**SWBAT calculate population mean (expected value) and standard deviation.

**Unit Assessment:**Analyze the normal distribution of ACT scores in Louisiana and USA.

**Lesson Plans:**

Lesson Number | Number of Days | Lesson Objective | Lesson Assessment | Benchmark or Standards |
---|---|---|---|---|

LP1 | 3 | Acquring & Integrating LPsSWBAT describe properties of normal distributions (e.g. mean, standard deviation, and empirical rule). | Quiz: Estimate probability based on empirical rule (1 problem calculating, 1 problem describing); sketch normal curves given mean and standard deviation (2 problems); describe properties of normal distribution (1 problem). | Indiana PS 1.1, 2.7, 2.8, 3.1 |

LP2 | 4 | SWBAT calculate areas under standard normal curve using z-values. | Quiz: Sketch and calculate areas under standard normal curve using z-values (3 problems). | PS 1.1, 2.7, 2.8, 3.1 |

LP3 | 3 | SWBAT analyze normal distribution by converting to standard normal distribution. | Quiz: Convert x-intervals to z-intervals (2 problems); sketch areas under standard normal curve and find specified areas (2 problems). | PS 1.1, 2.7, 2.8, 2.10 |

1 | Traditional Test | |||

LP4 | 2 | Extending & Refining LPs: SWBAT analyze Consumer Reports info on sunscreen products based on normal distributions. | Quiz: Determine whether a third product is superior to the two products analyzed in class. | PS 1.1, 2.7, 2.8, 2.10 |

LP5 | 2 | SWBAT analyze medical lab test results based on normal distribution of values in healthy adults. | Quiz: Analyze lab results from a new patient using normal distribution of values. | PS 1.1, 2.7, 2.8, 2.10 |

LP6 | 2 | Using Knowledge Meaningfully LP SWBAT apply inverse normal distribution (look up area and find corresponding z value) to analyze test scores. | Analyze the normal distribution of ACT scores in Louisiana and USA. | PS 1.1, 2.7, 2.8 |

1 | Performance Assessment | Part I: Write two multiple choice questions (with at least 4 answer choices each) based on the LP6 class work on the ACT score distribution. Each question should include detailed math and explanation for the correct answer. It should also include an explanation of the common mistakes that were made to generate the other incorrect answer choices. Part II: Perform a similar analysis of national SAT scores in math section and critical reading section. | PS 1.1, 2.7, 2.8, 3.1 | |

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