chapter 6.1 and 6.2

prob/stats

properties of normal curve

- are so numerous that some mathematicians refer to is as "a veritable Boy Scout Knife of statistics"

- 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

the parameters that control the shape of a normal curve are the mean u and the standard deviation o. when u and o are specified a specific normal curve is determined. in brief u locates the balance point and o determines the extent of the spread.

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standard scores

a standard score or z score of a measurement 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 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

- this is also known as the standard score gives the number of standard deviations between the original measurement x and the mean u of the x distribution.

- 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.