State the seven properties of the normal curve.
1) The normal curve is symmetric about its mean,
2) Because mean = median = mode (for qualitatitve data), the normal curve has a single peak and the highest point occurs at
3) The normal curve has inflection points at
and
4) The area under the normal curve is 1.
5) The area under the normal curve to the right of
equals the area under the normal curve to the left of
, which equals 0.5.
6) As "x" increases without bound (gets larger and larger), the graph approaches, but never reaches, the horizontal axis. As "x" decreases without bound (gets more and more negative), the graph approaches, but never reaches, the horizontal axis.
- 7) The Empirical Rule:
- Approximately 68% of the area under the normal distribution curve is between and , approximately 95% of the area is between and , and approximately 99.7% of the area is between and .