Density Curves and the Normal Distributions Section 2.1

Density Curve Describes the overall pattern of a distribution. Always on or above horizontal axis. Has area of exactly 1 underneath.

Median The median of a density curve is the equal areas point

Mean The mean of a density curve is the balance point

Mean and Median Equivalent for a symmetric curve. The mean of a skewed curve is pulled away from the median in the direction of the long tail.

Normal Distributions Symmetric, single-peaked, and bell-shaped The inflection points of a normal distribution are located one standard deviation from the mean

68-95-99.7 Rule Empirical Rule In the normal distribution, 68% of the observations fall within one standard deviation, 95% of the observations fall within two standard deviations, 99.7% of the observations fall within three standard deviations.

Practice Problems pg. 83 #2.2-2.4 pg. 89 #2.6-2.9 pg. 90 #2.11-2.15