Statistics, Chapter 3: The Normal Distribution

What is a normal distribution?

Is a smooth, symmetrical, bell-shaped curve.

Are all the same and located at the center…

Mean, median, and mode

What is the total area under the curve?

1.0 (or 100% of the data)

The curve never touches the horizontal axis…

it extends infinitely in both directions.

What is the empirical rule?

States that for normal distribution, 68% falls under one standard deviation. 95% falls under two standard deviations while 99.7% falls under three standard deviations.

Population mean symbol

Population standard deviation symbol 

Standard score symbol

z

Which statement best describes the normal curve?

It is symmetric and bell-shaped

About what percent of data fall between (Z = -2) and (Z = +2)?

95%

Approximately what percent of scores fall outside +2 SDs?

5%

If a test score has (Z = +2), the score is:

Two SDs above the mean

A psychology student earns a test score with Z = -2. What does this indicate?

The score is 2 SDs below the mean.