AP Statistics Chapter 2 - Describing Location in a Distribution

variable x

If a(n) ________ has any normal distribution N (μ, σ) with mean μ and standard deviation σ, then the standardized variable.

AP Statistics Chapter 2 Describing Location in a Distribution 2.1

Measures of Relative Standing and Density CurvesDensity CurveA density curve is a curve that is always on or above the horizontal axis, and has area exactly 1 underneath it.A density curve describes the overall pattern of a distribution

Normal Distributions A normal distribution is a curve that is mound-shaped and symmetric based on a continuous variable adheres to the 68-95-99.7 RuleThe 68-95-99.7 Rule In the normal distribution with mean μ and standard deviation σ

68% of the observations fall within 1σ of the mean μ. 95% of the observations fall within 2σ of the mean μ. 99.7% of the observations fall within 3σ of the mean μ

2.2

Normal DistributionsStandardizing and z-Scores If x is an observation from a distribution that has mean μ and standard deviation σ, the standardized value of x is