Section 2.2

Normal curves

An important class of density curves that are symmetric, single-peaked, and bell-shaped.

Normal distribution

A distribution described by a Normal density curve. Any particular Normal distribution is completely specified by two numbers: its mean (/u) and its standard deviation (o~). The mean of a Normal distribution is at the center of the symmetric Normal curve.

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

In a Normal distribution with mean (/u) and standard deviation o~:
- Approximately 68% of the observations fall within (+/-) o~ of the mean /u.
- Approximately 95% of the observations fall within (+/-) 2o~ of /u.
- Approximately 99.7% of the observations

Chebyshev's Inequality

States that in any distribution, the proportion of observations falling within k standard deviations of the mean is at least 1 - (1/k^2).
Ex) If k=2, Chebyshev's inequality tells us that at least 1 - (1/2^2) = 0.75 of the observations in any distribution

Standard Normal curve

A Normal curve that has is standardized such that it has a mean of 0 and a standard deviation of 1.

Standard Normal distribution

The standard Normal distribution is the Normal distribution with mean 0 and standard deviation 1. A standardized version of a normal distribution.
If a variable x has an Normal distribution N(/u,o~) with mean /u and standard deviation o~, then the standar

The standard Normal table

The standard Normal table is a table of areas under the standard Normal curve. The table entry for each value z is the area under the curve to the left of z.

Normal probability plot

Used to assess whether a data set follows a Normal distribution. To make a Normal probability plot, (1) arrange the data values from smallest to largest and record the percentile of each observation, (2) use the standard Normal distribution to find the z-