Chapter 6: Normal Distributions

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Presentation transcript:

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

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)

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 = 3.1416 e = 2.7183

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

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.