AII.11 
The student will identify properties of a normal distribution and apply those properties to determine probabilities associated with areas under the standard normal curve. 

Essential Knowledge and Skills 
 Identify the properties of a normal probability distribution.
 Describe how the standard deviation and the mean affect the graph of the normal distribution.
 Compare two sets of normally distributed data using a standard normal distribution and zscores.
 Represent probability as area under the curve of a standard normal probability distribution.
 Use the graphing calculator or a standard normal probability table to determine probabilities or percentiles based on zscores.

Essential Understandings 
 A normal distribution curve is a symmetrical, bellshaped curve defined by the mean and the standard deviation of a data set. The mean is located on the line of symmetry of the curve.
 Areas under the curve represent probabilities associated with continuous distributions.
 The normal curve is a probability distribution and the total area under the curve is 1.
 For a normal distribution, approximately 68 percent of the data fall within one standard deviation of the mean, approximately 95 percent of the data fall within two standard deviations of the mean, and approximately 99.7 percent of the data fall within three standard deviations of the mean.
 The mean of the data in a standard normal distribution is 0 and the standard deviation is 1.
 The standard normal curve allows for the comparison of data from different normal distributions.
 A zscore is a measure of position derived from the mean and standard deviation of data.
 A zscore expresses, in standard deviation units, how far an element falls from the mean of the data set.
 A zscore is a derived score from a given normal distribution.
 A standard normal distribution is the set of all zscores.


Vertical Articulation 
 SOL A.9  given a set of data, interpret variation in real‐world contexts/calculate/interpret mean absolute deviation/standard deviation /zscores.
 SOL AFDA.7  a) characteristics of normally distribution of data; b) percentiles;
c) normalizing data, using zscores; d) area under standard norm curve/ probability

Instructional Materials 
 VDOE ESS Lesson: Normal Distributions  Statistics (PDF)  Analyzing and using the standard normal curve (Word)
 Notes: Virginia Department of Education Technical Assistance documentation Algebra 1 (pdf)
 Notes: Virginia Department of Education Technical Assistance documentation Algebra 2(pdf)

Real World Lessons 

Practice 
 VDOE ESS: Statistics Review (pdf)
 VDOE ESS: Normal Distribution Exploration 1 (pdf)
 VDOE ESS: Normal Distribution Exploration 2 (pdf)
 VDOE ESS: Normal Distribution Exercises (pdf)
 VDOE ESS: Normal Distribution Exploration 3 (pdf)

SelfAssessments 
 SOL MiniQuiz: AII.11  Normal Distribution

Skills 
 JMU Pivotal Question: Normal Curves (doc)
 JMU Pivotal Question: Probability as Area Under the Curve (doc)

Videos 
 Video Tutor  Using a Normal Distribution
 Video Tutor  Using Standard Normal Curve
 Video Tutor  Finding Standard Deviation
 Video Tutor  Using Standard Deviation

Explore
Learning 
 None

Websites 
 Notes: Using the TI for find Normal Probability Distribution

Common Core
Standards 
