Lesson Plan: Approximating a Binomial Distribution Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to approximate a binomial distribution with a normal distribution.

Objectives

Students will be able to

  • understand how a binomial distribution approximates to a normal distribution and the conditions under which the approximation is valid,
  • use the approximation of a normal distribution to find probabilities or 𝑥-values of a binomial distribution,
  • solve binomial distribution approximation problems involving real-life contexts,
  • calculate the percentage error when using a normal distribution to approximate a binomial distribution.

Prerequisites

Students should already be familiar with

  • the normal distribution, including its properties, finding probabilities, 𝑥-values, and unknown parameters, and standardizing using transformations,
  • continuous and discrete random variables,
  • the binomial distribution, including its properties, finding probabilities, 𝑥-values, and unknown parameters, and finding an unknown number of trials,
  • the mean 𝜇 and the standard deviation 𝜎,
  • basic probability rules.

Exclusions

Students will not cover

  • using tables to calculate probabilities or 𝑥-values using the normal distribution as an approximation for the binomial distribution,
  • proof of the normal distribution,
  • hypothesis testing related to the normal distribution.

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