10.2 Normal Distributions

What makes a distribution normal

1. Normal distributions are symmetric around their mean.
2. The mean, median, and mode of a normal distribution are
equal.
3. The area under the normal curve is equal to 1.0.
4. Normal distributions are denser in the center and less dense in
the tails.
5. Normal distributions are defined by two parameters, the mean
(μ) and the standard deviation (σ).
6. 68% of the area of a normal distribution is within one standard
deviation of the mean.
7. Approximately 95% of the area of a normal distribution is
within two standard deviations of the mean.

x̄ vs μ (mew)

x̄ is the sample mean and μ is the population mean

empirical rule

The ____, also known as the three-sigma rule or the 68-95-99.7 rule, is is a statistical rule that states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ)

empirical rule graph