APEX AP Stats 2.1 Overview Intro to the Normal Distribution Study Guide

normal distribution

A symmetric distribution where the mean, median, and mode are all the same.

What characteristics go with normal distributions?

1. graph arises naturally

2. Shows when you draw samples form large populations

3. Useful in data analysis

4. Can be modeled by a bell-shaped density curve

Density curve

describes the shape of a distribution in which the total area is 1

What does the area under a density curve represent?

The area under a specific part of the curve within some range of values equals the proportion of total observations in the distribution falling within that range.

Normal curve

density curve that models a population distribution

What determines the center peak and height of a normal curve?

The population mean determines the location of the center peak and height of the curve.

What influences the height and spread of a normal curve?

The population standard deviation determines the height and spread of the curve.

What are inflection points in the context of a normal distribution?

points where the curvature of the slope first appears to change.

Does a normal distribution touch the x-axis?

no

Empirical Rule; 68-95-99.7 Rule

describes the areas and relative frequencies present in a normal distribution; 68%=1 standard deviation of the mean, 95%=2 standard deviations of the mean, 99.7%=3 standard deviations of the mean