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Understanding the Normal Distribution in Introductory Statistics

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This chapter explores the fundamental properties of the normal distribution, essential for understanding its role in statistics. Key features include the bell-shaped, symmetric nature of the curve, the total area under the curve equating to 1, and its significance in probability calculations. The mean and median coincide at the center. Additionally, the chapter explains z-scores, indicating how many standard deviations an observation is from the mean, and introduces the standard normal distribution, where the mean is 0 and standard deviation is 1. Techniques for finding probabilities and percentiles are also covered.

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Understanding the Normal Distribution in Introductory Statistics

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  1. Chapter 9 – The Normal Distribution Math 22 Introductory Statistics

  2. Properties of the Normal Distribution Basic properties of all normal distributions: • The total area under the curve is equal to 1 • The distribution is bell shaped and symmetric • The curve extends to infinity in both directions • The distribution is centered at the mean • The mean is equal to the median

  3. Properties of the Normal Distribution • The area under the curve between any two points of the normal distribution is equal to the probability of observing a value between those two points.

  4. z - Score • Number of standard deviations an observation resides from the mean.

  5. The Standard Normal Distribution • The mean is equal to 0. • The standard deviation is equal to 1.

  6. Finding Probabilities • Finding probabilities using the TI – 83. • Percentiles

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