The Normal Distribution

Statistics · Axiom Academy

LESSON The Normal Distribution Understanding the bell curve, its parameters, and the empirical rule The normal distribution has a distinctive symmetric, bell-shaped curve. The highest point of the curve represents the most probable value, and probability decreases as we move away from the center in either direction. 2. Parameters: Mean (μ) and Standard Deviation (σ) The normal distribution is completely determined by two parameters: The center of the distribution Determines the location on the number line Measures the spread of the distribution Determines the width of the bell curve Watch how changing these parameters affects the shape and position of the normal curve: 3. The Empirical Rule (68-95-99.7 Rule) One of the most useful properties of the normal distribution is that we can predict what percentage of data falls within certain distances from the mean: 68% of data falls within 1 standard deviation (μ ± σ) 95% of data falls within 2 standard deviations (μ ± 2σ) 99.7% of data falls within 3 standard deviations (μ ± 3σ)

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