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Normal Distributions

Distributions whose shapes are unimodal and approximately symmetric can be modeled by a normal distribution. In the lessons in this unit, students investigate families of normal distributions and their characteristics, create and analyze normal probability plots, investigate z-scores, and transform different distributions of univariate data.

Statistics: Normal Distributions Activities

Title Type

Exploring the Normal Curve Family

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.

Alignments  Standards  |  Textbook  
  • 4903


This lesson involves finding the area under the standard normal curve with mean 0 and standard deviation 1 for a given distance from the mean and compare this to the area under the curve for another member of the family of normal curves.

Alignments  Standards  |  Textbook  
  • 5405

Assessing Normality

In this activity, students will learn four characteristics of a normal curve: the distribution is symmetric and mound-shaped; the mean and median are approximately equal; the distribution meets the 68-95.5-99.7 rule; and the normal probability plot is linear. They will use these to determine if a data set it normal.

Alignments  Standards  |  Textbook  
  • 4657

Normal Probability Plot

This lesson involves creating a normal probability plot for several data sets involving height to examine the appearance of such plots when the distribution is approximately normal.

Alignments  Standards  |  Textbook  
  • 3964

Looking Normal

This lesson involves examining multiple samples taken from a single approximately normal population.

Alignments  Standards  |  Textbook  
  • 3880


Students use the area to the left of a value in a normal distribution to find its percentile and then reverse the process to find the value for a given percentile.

Alignments  Standards  |  Textbook  
  • 4395

Transforming Univariate Data

This lesson involves square root, logarithmic, square, and exponentiation transformations of skewed univariate data using a given data set.

Alignments  Standards  |  Textbook  
  • 3729
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