# Chapter 6

## Empirical Rule

for a distribution that is symmetrical and bell shaped ( in particular, for a normal distribution)

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

## Control Chart

How to make a control chart

1. find the u and standard deviation o of the x distribution by:

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

(b) use 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 lines at u +/- 2o and u+/- 3o

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

## Out of Control Signals

out of control signal 1: one point falls beyond the 3o level

2: a run of nine consecutive points on one side of the center line

3: at least two of the three consecutive points lie beyond the 2o level on the same side of the center line

## Standard Scores or Z scores

Standard scores tell us:

a standard score or z score of a measrement tels us the number of standard deviations the measurement is from the mean.

a standard score close to 0 tells us the measurement is near the mean of the distribution

a positive standard score tells us the measurement is above the mean

a negative standard score tells us the measurement is below the mean