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
- 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.
out of control signals
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
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.