# 6.1 and 6.2

### Nejad Yazbeck

## properties of normal curve

**Properties of a Normal Distribution**

- The normal curve is symmetrical about the mean μ;
- The mean is at the middle and divides the area into halves;
- The total area under the curve is equal to 1;
- It is completely determined by its mean and standard deviation σ

**procedure**

- Find the mean u and standard deviation of the x distribution by using past data from a period during which the process was in control

2. create a graph in which the vertical axis represents x values and the horizontal axis represents time

draw a horizontal line at height mean and horizontal, dashed control-limit line at mean + 2mean and mean +- 3 mean

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

## control chart

**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.

control chart offers a brief overview of the most common charts and a discussion of how to use the Assistant to help you choose the right one for your situation. And if you're a control chart neophyte and you want more background on why we use them, check out

**Control Charts Show You Variation that Matters.**

## M and standard deviation

We see that a general normal curve is smooth and symmetrical about the vertical line extending upward from the mean m.

Notice that the highest point of the curve occurs over m. If the distribution were graphed on a piece of sheet metal, cut out, and placed on a knife edge, the balance point would be at m.

We also see that the curve tends to level out and approach the horizontal (x axis) like a glider making a landing.

## scores calculating

If the original distribution of x values is normal, then the corresponding z values have a normal distribution as well. The z distribution has a mean of 0 and a standard deviation of 1. The normal curve with these properties has a special name.

Any normal distribution of x values can be converted to the standard normal distribution by converting all x values to their corresponding z values. The resulting standard distribution will always have mean m = 0 and standard deviation s = 1.