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Standard Normal Distribution and Probability in Behavioral Sciences: Lecture Notes, Study notes of Statistics for Psychologists

English and Foreign Languages UniversityStatistics for Psychologists

Lecture notes on the standard normal distribution and probability in the context of the behavioral sciences. Topics covered include the definition and mathematical function of the standard normal distribution, facts about the distribution, and the use of the unit normal table to compute probabilities. Additionally, the document discusses the concept of probability, including its properties and interpretation.

Typology: Study notes

2011/2012

Uploaded on 11/21/2012

ashakiran
ashakiran 🇮🇳

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Basic Statistics for
The Behavioral Sciences
LECTURE NOTES
1
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Basic Statistics for

The Behavioral Sciences

LECTURE NOTES

Ch. 6. Standard normal distribution and Probability

I. Standard Normal Distribution A. Definition; a particular normal distribution with μ = 0, and σ = 1 obtained by the z- transformation of different normal distributions. B. Mathematical function

y = f(z) = 2

2

z e

−

where, y = height on the ordinate (Y-axis), z = point on the abscissa (Z-axis), π ≈ 3.14....., e ≈ 2.72......

C. Some facts about SND

  1. We can transform only normal distributions to the standard normal distribution with the z- score formula. Why?
  2. We can use areas under the standard normal curve as probabilities or proportions of the total cases.
  3. We use calculus to determine the area under curve, integrating the normal equation to find the area.===> No closed form solutions.
  4. But, someone who loved you and me made a table for us!!!===> Unit Normal Table. D. Unit Normal (z-score) table.
  5. We can compute the probability of any interval associated with a z-score using the table.
  6. Examples a) What proportion of the scores fall between z = 0 and 1? b) proportion beyond z = 2. c) p(1≤z≤2)=? d) p(-.5≤z≤1)=?