### Course 4 Unit 5 - Binomial Distributions and Statistical Inference 1st Edition

Binomial Distributions and Statistical Inference is the final unit of the statistics and probability strand of the Contemporary Mathematics in Context program. This unit draws together concepts from both statistics and probability. (See the descriptions Course 4 Units.)

#### Unit Overview

This unit extends student understanding of the binomial distribution, including its exact construction and how the normal approximation to the binomial distribution is used in statistical inference.

 Unit Objectives To develop the binomial probability formula and know when it can be used To examine the formulas for the mean and standard deviation of a binomial distribution To use the normal approximation to estimate binomial probabilities To understand the logic of the z-test for a proportion To distinguish between an experiment, a survey, and an observational study To know the characteristics of a well-designed experiment To apply the z-test for the difference of two proportions to experiments

#### Sample Overview

This sample material consists of the two investigations of Lesson 2, "Characteristics of Binomial Distributions." In the first investigation, students examine the shape, center, and spread of binomial distributions for the number of and the proportion of successes. In the second investigation, students examine and apply the simple formulas for the mean and standard deviation of a binomial probability distribution.

#### Instructional Design

Throughout the curriculum, interesting problem contexts serve as the foundation for instruction. As lessons unfold around these problem situations, classroom instruction tends to follow a common pattern as elaborated under Instructional Design.

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