# Chapters 6.1 & 6.2

## Properties of Normal Curve

Normal Distribution Curves are symmetrical bell-shaped curves possessed of distinct characteristics.

## Empricial Rule

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviation of the mean.

## Control Chart

The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit. These lines are determined from historical data.

## Out of Control Signals

We call the system out of control if at least one of the three events occur

• Out of Control Signal 1: At least one point falls beyond the 3s level.
• Out of Control Signal 2: A run of nine consecutive points is on the same side of the center line (usually the mean).
• Out of Control Signal 3: At least two of three consecutive points lie beyond the 2s level on same side of the center line (usually the mean).

## Standard Scores

The standard score (more commonly referred to as a z-score) is a very useful statistic because it (a) allows us to calculate the probability of a score occurring within our normal distribution and (b) enables us to compare two scores that are from different normal distributions.

## Z-Scores Calculating

The standard score (more commonly referred to as a z-score) is a very useful statistic because it (a) allows us to calculate the probability of a score occurring within our normal distribution and (b) enables us to compare two scores that are from different normal distributions.