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Henrico County Public Schools, Virginia
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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 z-scores. 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 z-scores. Essential Understandings A normal distribution curve is a symmetrical, bell-shaped 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 z-score is a measure of position derived from the mean and standard deviation of data. A z-score expresses, in standard deviation units, how far an element falls from the mean of the data set. A z-score is a derived score from a given normal distribution. A standard normal distribution is the set of all z-scores.
Vertical Articulation
1. SOL A.9 - given a set of data, interpret variation in real‐world contexts/calculate/interpret mean absolute deviation/standard deviation /z-scores.
2. SOL AFDA.7 - a) characteristics of normally distribution of data; b) percentiles; c) normalizing data, using z-scores; d) area under standard norm curve/ probability
Instructional Materials
1. VDOE ESS Lesson: Normal Distributions - Statistics (PDF) - Analyzing and using the standard normal curve (Word)
2. Notes: Virginia Department of Education Technical Assistance documentation Algebra 1 (pdf)
3. Notes: Virginia Department of Education Technical Assistance documentation Algebra 2 (pdf)
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Common Core Standards
 S-ID.4