# chapter 6 part 1-2

## properties of a normal curve

- the curve is bell-shaped, with the highest point over the mean

- the curve is symmetrical about a vertical line through the mu

- the curve approaches the horizontal axis but never touches or crosses it

- the inflection (trasition) points between cupping upward and downward occur above the mu+o and mu-o

- the area under the entire curve is 1

## empirical rule

- for distribution that is symmetrical and bell-shaped (in particular, for a normal distribution)

- 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% (or almost all) of the data values will lie within 3 standard deviations on each side of the mean

## finding standard mean and standard deviation

• Work out the Mean (the simple average of the numbers)
• Then for each number: subtract the Mean and square the result
• Then work out the mean of those squared differences.
• Take the square root of that and we are done!

## control chart

The control chart is a graph used to study how a process changes over time. Data are plotted in time order and they always have a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit.