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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
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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 = 3.1416e = 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.