# Chapter 6 Sections 6.1-6.2

## Properties of a Normal Curve

1) The curve is bell-shaped, with the highest point over the mean

2) The curve is symmetrical about a vertical line through the mean

3) The curve approaches the horizontal axis but never touches or crosses it

4) The inflection (transition) points between cupping upward and downward occur above the mean + standard deviation and mean - standard deviation

5) The area under the entire curve is 1

## Section 6.1 Empirical Rule

For a distribution that is symmetrical and bell-shaped

- Approximately 68% of the data values will lie within 1 standard deviation on each side of the mean

- Approximately 95% of the data values will lie within 2 standard deviations on each side of the mean

- Approximately 99.7% (or almost all) of the data values will lie within 3 standard deviations on each side of the mean

## Out of Control Signals

Out-of-Control Signal I: One point falls beyond the 3 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 2 standard deviation level on the same side of the center line

## Z-Scores-Calculating

The z value gives the number of standard deviations between the original measurement x and the mean of the x distribution