# MATH 10041 Chapter Notes - Chapter 6: Central Limit Theorem, Gaussian Function, Standard Deviation

6.2: The Normal Model

Normal Model: the most widely used probability model for continuous numerical values

• Provides a very close fit

• The Central Limit Theorem links the Normal model to several key statistical ideas, which

provides good motivation for learning this model

Normal Curve/Normal Distribution: the curve drawn on histograms

• The curve provided a model that pretty closely described a good number of continuous-

valued data distributions

• Unimodal and Symmetric Distributions: symmetric distributions have histograms whose

right and left sides are roughly mirror images of each mother. Unimodal distributions

have histograms with one mound

• Bell Curve: the normal or Gaussian curve is also called the bell curve

•

Mean of a probability distribution: represented by the Greek letter μ pronounced “Mu”

Standard deviation of a probability distribution: represented by sigma

• The exact shape of the Normal distribution is determined by the values of the mean and

the standard deviation

• The normal distribution is symmetric and the mean is the exact center of the

distribution

• The standard deviation determines whether the normal curve is wide and low or narrow

and tall

•

Standard Normal Model: the normal model with mean 0 and standard deviation 1