# Lessons 6.1 and 6.2

## Properties of a Normal Curve

1. The curve is bell-shaped with highest poing over the mean.
2. The curve is symmetrial about a vertical line through the mean.
3. The curve approaches the horizontal axis never touches or crosses itl
4. 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

1. FInd the mean and stardard deviation of the x distribution by

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

1. Signal I- One point falls beyond the 3 standard deviation level

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

The z value or z score (also known as standard score) gives the number of standard deviation between the original measurement x and the mean h of the x distribution.

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