# Chapter 6

### Normal curves And Sampling Distributions Lessons 1 and 2

## Empirical Rule

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

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.

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

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