the data fall within two standard deviations of the mean, and approximately 99.7 percent of the data fall within three standard deviations of the mean. This is often referred to as the Empirical Rule or the 68-95-99.7 rule. NOTE: This chart illustrates percentages that correspond to subdivisions in one standard deviation increments. Percentages for other subdivisions require the table of Standard Normal Probabilities or a graphing utility. The mean and standard deviation of a normal distribution affect the location and shape of the curve. The vertical line of symmetry of the normal distribution falls at the mean. The greater the standard deviation, the wider (“flatter” or peaked”) the distribution of the data. “less A derived from a particular data value tells how many standard deviations that data value falls above or below the mean of the data set. It is positive if the data value lies above the mean and negative if the data value lies below the mean. A standard normal distribution is the set of all The mean of the z-scores. data in a standard normal distribution is 0 and the standard deviation is 1. This allows for the comparison of unlike normal data. The table of Standard Normal Probabilities and graphing utilities may be used to determine normal distribution probabilities. a (z), the table of Standard Normal Probabilities (z-table) z-score shows the area under the curve to the left of This area represents the z. proportion of observations with a less than the one specified. z-score Table rows show the whole number and tenths place. Table z-score’s columns show the hundredths place.
the data fall within two standard deviations of the mean, and approximately 99.7 percent of the data fall within three standard deviations of the mean. This is often referred to as the Empirical Rule or the 68-95-99.7 rule. NOTE: This chart illustrates percentages that correspond to subdivisions in one standard deviation increments. Percentages for other subdivisions require the table of Standard Normal Probabilities or a graphing utility. The mean and standard deviation of a normal distribution affect the location and shape of the curve. The vertical line of symmetry of the normal distribution falls at the mean. The greater the standard deviation, the wider (“flatter” or “less peaked”) the distribution of the data. A derived from a particular data value tells how many standard deviations that data value falls above or below the mean of the data set. It is positive if the data value lies above the mean and negative if the data value lies below the mean. A standard normal distribution is the set of all z-scores. The mean of the data in a standard normal distribution is 0 and the standard deviation is 1. This allows for the comparison of unlike normal data. The table of Standard Normal Probabilities and graphing utilities may be used to determine normal distribution probabilities. a z-score (z), the table of Standard Normal Probabilities (z-table) shows the area under the curve to the left of z. This area represents the proportion of observations with a z-score less than the one specified. Table rows show the z-score’s whole number and tenths place. Table columns show the hundredths place.
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