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Normal Distributions for Probability Analysis

Explore bell-shaped continuous probability distributions, properties of the normal curve, and the Empirical Rule for data values within standard deviations. Learn how to interpret graphs and calculate probabilities accurately.

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Normal Distributions for Probability Analysis

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  1. Chapter 6: Normal Distributions Section 1: Probability Distributions Graphs of Normal

  2. Properties of a Normal Curve • represents continuous probability distributions • bell-shaped with the highest point over the mean • symmetrical about a vertical line through the mean (Continued on next slide)

  3. curve approaches the horizontal axis but never touches or crosses it • area beneath the curve is exactly one • probability distribution given by the formula f(x)= π = 3.1416e = 2.7183

  4. the portion of the area under the curve above a given interval represents the probability that a measurement will lie in that interval

  5. Empirical Rule For a distribution that is symmetrical and bell-shaped (a normal distribution) : * Approximately 68% of the data values will lie within one standard deviation on each side of the mean. * Approximately 95% of the data values will lie within two standard deviations on each side of the mean. * Approximately 99.7% of the data values will lie within three standard deviations on each side of the mean.

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