Education Technology

Exploring the Normal Curve Family

Updated on 07/03/2014

Activity Overview

Students will investigate the relationship of the equation of a normal curve to its graph. They will use a slider to change the values of two parameters, μ and σ, to investigate their effects on the normal curve, noting in particular that μ represents the location of the mean and that σ represents the distance from the mean to the curve at the point of inflection.

Objectives

  • Students will identify the three defining characteristics of a normal curve related to shape, center, spread, and area.
  • Students will recognize that normal curves form a family whose members share these same characteristics.

Vocabulary

  • normal curve
  • mean
  • standard deviation
  • point of inflection
  • density functions

About the Lesson

This lesson involves investigating the relationship of the equation of a normal curve to its graph.
As a result, students will:

  • Identify the axis of symmetry as the line x =, the mean of the distribution represented by the normal curve, and the standard deviation as the distance from that line to the point of inflection.
  • They will use a slider to change the values of two parameters, m and s to investigate their effects on the normal curve, noting in particular that m represents the location of the mean and that s represents the distance from the mean to the curve at the point of inflection.
  • Estimate the area under a normal curve graphed on a coordinate grid and investigate how this area changes as the mean and standard deviation are changed.