|Normal and Standard Normal Distributions |
- e - a constant approximately equal to 2.718281828454590, as defined below.
- z - the variable used to indicate workis with the standard normal distribution having a mean of 0 and a standard deviation of 1.
- the ratio of the circumference of a circle to its diameter, about 3.14159 or 22/7.
- NORMAL DISTRIBUTIONS - or Gaussian distribution, a continuous probability distribution (so the area under the curve equals 1),
where the mean, mode, median are all the same, so the data gathers about a center making a symmetric bell-shaped curve.
Many data points -- heights of people, lengths of fish, errors measurements, standardized test scores have normal distributions.
- STANDARD NORMAL DISTRIBUTION - a normal distribution having a mean of 0 and a standard deviation of 1. It is very useful in computing, and looking up, probabilities, comparing samples and populations, and analysis and hypothesis testing.
- STANDARD NORMAL TABLE OF PERCENTS/PROBABILITIES - uses z-scores and their probabilities.
- CUMULATIVE STANDARD NORMAL DISTRIBUTION - uses z-scores and their probabilities beginning with z=-3 and ending with z= 3 but, lists the sum of the probabilities from z = -3 to the desired z-score.
- BELL-SHAPED CURVE - a normal distribution. It looks like a symmetric bell sitting on a table. The scores are piled in the center and trail off at the upper and lower range of variables.
- WITHIN A SPECIFIC STANDARD DEVIATION OF THE MEAN - a range of scores centered about the mean and, in either direction, not farther on the number line than the specified number of standard deviations.
ex. on the standard normal number line, "within 1 standard deviation of the mean" means, from -1 to 1, - 1 < z < 1, and includes about 68% of the scores
ex. on the normal number line, "within 3 standard deviation of the mean" means, from -3 to 3, - 3 < x < 3, and includes about 99.7% of the scores.
- CHEBYCHEV'S RULES -- for any distribution, the percent of scores within k standard deviations of the mean, k > 0, is 1/k2