# chapter 6.1 and 6.2

### prob/stats

## properties of normal curve

- normal curve possesses a shape very much like the cross section of a pile of dry sand.

- bell-shaped curve is shaped like blacksmiths would sometimes use a pule of dry sand in the construction of a mold for a bell

important properties of a normal curve

- the curve is bell-shaped with the highest point over the mean u.

- the curve is symmetrical about a vertical line through u.

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

- the inflection (transition) points between cupping upward and downward occur above u+o and u-o

- the area under the entire curve is 1

## M and O

## keep learning not done yet

## empirical rule for a distribution that is symmetrical and bell-shaped (in particular for a normal distribution): - approximately 68% of 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 | ## control chart - a random variable z is said to be in statistical control if it can be described by the same probability distribution when it is observed at successive points in time. - control charts combine graphic and numerical descriptions of data with probability distributions. | ## out of control signals signal I: one point falls beyond the 3o level signal II: a run of nine consecutive points on one side of the center line (the line at target value u) signal III: at least two of three consecutive points lie beyond the 2o level on the same side of the center line |

## empirical rule

- approximately 68% of 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

## control chart

- control charts combine graphic and numerical descriptions of data with probability distributions.

## last section to learn keep on going

## standard scores

- a standard score close to zero tells us the measurement is near the mean of the distribution.

- a positive standard score tells us the measurement is above the mean.

- a negative standard score tells us the measurement is below the mean.

## z-scores-calculating using that and appendix with probabilities

- an x value in the original distribution that is above the mean u has a corresponding z value that is positive. again this makes sense because a measurement above the mean would be a positive number of standard deviations from the mean.