APEX AP Stats 2.1.2 The Normal Curve Study Guide

Normal Curve

aka probability distribution; symmetric and bell-shaped curve

What can you tell from the normal curve?

frequency declines as you get farther away form the mean

What things affect how the normal curve appears? 1. more classes = smoother top 2. most cases are around the population mean

Is a normal curve an actual distribution?

no, it's a model of the distribution

Normal distribution

A function that represents the distribution of variables as a symmetrical bell-shaped graph.

Central Limit Theorem

demonstrates a strong link between normal distributions and sampling

Characteristics of a normal distribution

1. mean, median, and mode are all in the same place 2. Left and right tails never touch the x-axis 3. Can be wide and short or tall and skinny 4. Total area under the curve is the same and =1 (the same for all density curves) 5. Can have different standard deviations and the same mean, just makes the graphs height/length different

What does the area under the normal distribution show?

the chances something will happen

Inflection points

2 points that are a 1 standard deviation from the mean and will give you a percentage of the area if you calculate the area between them

Where are the inflection points on a normal distribution?

at the 68% point

The Empirical Rule (aka 68-95-99.7 Rule) formula

population mean + population standard deviation=the number of observations in that area