# Lessons 6.1 and 6.2

### Amari Bellard

## Properties of a Normal Curve

- The curve is bell-shaped with highest poing over the mean.
- The curve is symmetrial about a vertical line through the mean.
- The curve approaches the horizontal axis never touches or crosses itl
- The inflection (transition) points between cuooing upwad and downward occur above the mean plus the standard deviation and the mean minus standard deviation.

## Empirical Rule

- Approximately 68% of the data values will lie within 1 standard deviation on each side of them
- Approximately 95% of the data values will lie within 1 standard deviation on each side of them
- Approximately 99.7% of the data values will lie within 1 standard deviation on each side of them

## Control Chart Procedure

a) using past data from a period during which the process was "in control" or

b) using specified "target" values for the mean and standard deviation

2. Create a graph in which the vertical axis represents x values and the horizontal axis represents time.

3. Draw a horizontal line at height h and horizontal, dashed control-limit lines at h plus/minus 2 times the standard deviation and h plus/minus 3 times the standard deviation.

4. Plot the variable x on the grpah in time sequence order. Use line segments to connect the points in time sequence order.

## Out-of-Control Signals

2. Singal II- A run of 9 consecutive points on one side of the center line

3. Signal III- At least two of three consecutive points lie beyond 2 standard deviation level on the same side of the center line

## Z Scores and Raw Scores

(number of standard deviations between the measurement and the mean)= (difference between the measurement and the mean/standard deviation)