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 = e =

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.