Chapter 6 Section 1 & 2

Properties of Normal Curve

1. Curve is bell-shaped with highest point over the mean

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

For a distribution that is a normal curve

- 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

a control chart for a random variable x is a plot of observed x values in time sequence order.

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

1. One point falls beyond the 3rd standard deviation level

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

also known as a 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