# Chapter 6 Section 1 & 2

### Landon Cormier

## Properties of Normal Curve

2. Curve is symmetrical about a vertical line through the mean

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

4. inflection(transition) points between cupping upward and downward

**Mean and Standard Deviation**

-mean is the highest point in the middle

-a whole standard deviation is 1 spot on each side of the mean

## Empirical Rule

- approximately 68% of the data values will lie within 1 standard deviation on each side of mean

- approximately 95% of the data values will lie within 2 standard deviation on each side of mean

- approximately 99.7% of data values will lie within 3 standard deviation on each side of mean

## Making a Control Chart

1. find the mean and standard deviation of x by:

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

b. using specified "target" values for 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 a height of the mean

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

## Out of Control Signals

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

3. at least 2 of 3 consecutive points lie beyond the second deviation level on the same side of center line

## Standard Scores

*z score*tells us the number of standard deviations the measurement is from the mean

- a standard score close to zero tells us the measurement is near the mean of distribution
- positive standard score tells us the measurement is above the mean
- negative standard score tells us the measurement is below the mean