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Easy Statistics Series 4: Normal Distribution

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Probabilities

  • A probability is a measure of the expectation that an event will occur.
  • Probabilities lie between 0 and 1.
  • We shall first explore this concept in terms that are familiar to you.

Normal Distribution

Forget the Formulation

The probability density function of normal distribution is:

normal_distribution_probability

Most students are suffering from understanding about this formulation. My suggestion is that you should forget about this formulation and focus on the shape and area of the normal distribution.

Shape of Normal Distribution

Normal distribution is symmetric “bell-shaped” distribution with unlimited range.

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Effect μ and σ

normal_u

Standard Normal Distribution

normal_standard

The normal distribution with µ=0 and σ=1 is called “standard normal distribution”.

normal_ares

Z-Scores

z_formulation

Example (Source: STAT170):

IQ is normal distributed with µ=100 and σ=15.

What’s the Z-Scores of person with IQ=130?

iq_z

z_cal

z-Table

z_table

Use_z_table

 

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