# 6.1 & 6.2

## Properties of Normal Curve

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

2. The curve is symmetrical about a vertical line through u.

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

4. The inflection (transition) points between cupping upward and downward occur aboce u +0 and u - o.

5. The area under the entire curve is 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 98% of the data values will lie within 2 standard deviations on each side of the mean.

approximately 99.7% of the data values will lie within 3 standard deviations on each side of the mean.

## Control Chart

a control chart for a random variable x is a plot of observed x values in time sequence order.

1. find the mean u and standard deviation o of the x distribution by using past data from period during which the process was in control or

b. using specified target values for u and o.

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 u and horizontal, dashed control-limit lines at u + 20 and u + 30.

4. plot the variable x on the graph in time sequence order. use line segments to connect the points in time sequence order.