![]() ![]() Once the scores of a distribution have been converted into standard or Z-scores, a normal distribution table can be used to calculate percentages and probabilities. The area to the left of a Z value of 2.5 is 0.9938 A Z-score of 2.5 represents a value of 2.5 standard deviations above the mean. ![]() Since the distribution has a mean of 0 and a standard deviation of 1, the Z column is equal to the number of standard deviations below (or above) the mean. In this version, the Z column contains values of the standard normal distribution the second column contains the area below Z. There are different versions of the standard normal curve table. Adding this deviation score to the mean: -24 + 50= 26.Multiplying the Z-score by the standard deviation (shown above as 10): -2.4 x 10= -24, and.In the example above, the raw score -2.4 can be transformed back into a raw score by: Determining the raw score by adding the mean to the deviation score.Determining the deviation score by multiplying the Z-score by the standard deviation, then.Transforming a Z-score back into raw scoreĪdditionally, a Z-score can be transformed into a raw score by: The Z-score of a raw score of 26, in this given distribution, is -2.4 (negative sign means that the score is below the mean). To calculate a Z-score, the mean and standard deviation are needed.įor example, if the mean of a normal distribution of class test scores is 50, and the standard deviation is 10, to calculate the Z-score for 26 the formula is applied: Where x is the standardised value- or value on the standard normal distribution, x is the value on the original distribution, µ is the mean of the original distribution, and o is the standard deviation of the original distribution. In order to be able to use this table, scores need to be converted into Z scores.Ī value from any normal distribution can be transformed into its corresponding value on a standard normal distribution using the formula: Statisticians have worked out tables for the standard normal curve that give the percentage of scores between any two points.This means that the standard normal distribution can be used to calculate the exact percentage of scores between any two points on the normal curve. ![]()
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