# Susan Verdin

### Chapter 6 Sec 1 and Sec 2

## Section 6.1

## Properties of a Normal Curve

*Important Properties of a normal curve are:*

- The curve is bell shaped, with the highest point over mean.
- The curve is symmetrical about a vertical line through mean.
- Curve approaches horizontal axis but never touches it.
- The inflection(transition) points between cupping upward and downward occur above mean + standard deviation and mean - standard deviation.
- The area under the entire curve is 1.

## The Mean and Standard Deviation

- On the graph, the mean is always in the middle.
- The left side of the mean is positive, and the right side is negative.
- The area between
*mean - SD and mean + SD*equals*34%* - The area between
*mean - 2SD and mean + 2SD*equals*13.5%* - The area between
*mean - 3SD and mean + 3SD*equals*2.35%* - Anything beyond is
*0.15%*

## The Empirical Rule

*68%*of data values lie within 1 standard deviation on each side of the mean.*95%*of data values lie within 2 standard deviations on each side of the mean.*99.7%*of all data values within 3 standard deviations on each side of the mean.

## Example of Bad Curve 1 This curve is not normal because it touches the horizontal axis and goes below the mean. | ## Example of Bad Curve 2 This curve is not normal because it touches the horizontal axis and goes below the mean. | ## Example of Bad Curve 3 This curve is not normal because it is not symmetrical. |

## Example of Bad Curve 1

This curve is not normal because it touches the horizontal axis and goes below the mean.

## Example of Bad Curve 2

This curve is not normal because it touches the horizontal axis and goes below the mean.

## Out-of-Control Signal I One point falls below the 3SD(standard deviation) level. | ## Out-of-Control Signal II A run of nine consecutive points on one side of the center line. | ## Out-of-Control Signal III At least two of three consecutive points lie beyond the 2SD level on the same side of the center line. |

## Section 6.2

## Z Scores, Standard Scores, and Raw Scores

A Z-Score is a statistical measurement of a score's relationship to the mean in a group of scores. A Z-Score of 0 means the score is the same as the mean. A Z-Score can also be positive or negative, indicating whether it is above or below the mean and by how many standard deviations. When given mean and SD, the data can be converted to Z-Scores, Raw scores, or Standard scores.