![]() ![]() ![]() The mean for the standard normal distribution is zero, and the standard deviation is one. Normal distributions follow the empirical rule, also called the 68-95-99.7 rule. Z-scores offer analysts a way to compare. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. In most large data sets, 99 of values have a Z-score between -3 and 3, meaning they lie within three standard deviations above or below the mean. ![]() Here we break the z-score into two parts, the left part is usually the units and tenths digits and. A z-score is measured in units of the standard deviation. A common approach to this is the cross-table arrangement. The mean of this distribution of z-scores has a mean of zero and a standard deviation of one. For example, the first data value of 3 lies 1.39 standard deviations below the mean. The standard normal distribution is a normal distribution of standardized values called z-scores. The z-score tells us how many standard deviations each data point lies from the mean. Recognize the standard normal probability distribution and apply it appropriately. ![]()
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