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

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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
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
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