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The Normal Distribution

Topic Review on "Title":

Normal Distribution: describes a set of observations whose graph is symmetric and unimodal.
Normal Curve: is a special density curve that characterizes the normal distribution.
Parameters: numbers that help specify the model.  For the normal distribution, the parameters are µ for the mean and σ for the standard deviation, written as N(µ, σ) .
Z-Score: standardized value of an observation that measures its distance from the mean.
68-95-99.7 Rule:  A sometimes termed the empirical rule, states that, in the Normal model: 68% of the observations in a distribution fall within 1 standard deviation of the mean, 95% of the observations in the distribution fall within 2 standard deviations of the mean, and 99.7% of the observations in the distribution fall within three standard deviations of the mean.

  • Normal quantile plot: A graph used to verify the normality of a distribution.
  • Standardize observations in order to compare values with different units.
  • z-score = (x - μ)/ σ
  • The z-score has no units. 
  • The z-score is an indication of how unusual a value is by how far away from the mean it is.
  • Standardizing shifts the mean to zero and standard deviation to 1. 
  • Standardizing data does not change the shape of the graph.
  • When working problems involving z-score and the 68-95-99.7 rule…draw a picture!
  • x = any given observation
  • σ =standard deviation
  • μ = mean
  • 68-95-99.7 Rule Used for finding the areas within a normal distribution. 


Rapid Study Kit for "Title":
Flash Movie Flash Game Flash Card
Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

"Title" Tutorial Summary :

This tutorial detailing normal distribution – describes a set of observations whose graph is symmetric and unimodal. Many important concepts such as why and how data values are standardized, how to use z-scores to calculate area under the normal curve, how to use the 68-95-99.7 Rule, how to calculate z-score based on given information and to identify normal distributions by their normal quantile plot are all clearly demonstrated.


Tutorial Features:

Specific Tutorial Features:

  • Step by step examples showing 68-95-99.7 rule is shown in this tutorial.
  • Examples displaying how to find the z-score are presented with the use of graphs.

Series Features:

  • Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
  • Definition slides introduce terms as they are needed.
  • Visual representation of concepts
  • Animated examples—worked out step by step
  • A concise summary is given at the conclusion of the tutorial.

"Title" Topic List:
  • Normal Distribution
  • Normal Curve
  • Parameters
  • Z-Score
  • 68-95-99.7 Rule
    • Normal quantile plot
    • z-score
    • Standardizing


See all 24 lessons in Introductory Statistics, including concept tutorials, problem drills and cheat sheets:
Teach Yourself Introductory Statistics Visually in 24 Hours

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