In a standard normal distribution, what percentage of values will be above 1.28?ġ. 89973, which means that the percentage of values less than 1.28 is 89.97%Įxample 2: Finding the percentage of values to the right of a Z-value Use the standard normal table to find the value to the left of 1.28.ģ. Draw a diagram: you are looking for the percentage of the graph to the left of 1.28.Ģ. In a standard normal distribution, what percentage of values will be less than 1.28?ġ. 0.7734 would be expressed as 77.34%.Įxample 1: Finding the percentage of values to the left of a Z score To obtain the probabilities, simply multiply the percentage by 100. For example, if you are looking for a Z score of 0.75, you will look at the intersection of 0.7 (Z column) and the column 0.05 (0.7 + 0.05= 0.75). If your Z score contains decimals, use the columns to the right. To read the table, find the Z score in the left column Z. The table gives the proportion to the left of a chosen Z-value of up to 2 decimal places. Calculate the proportion of scores between two Z-scores. Calculate the proportion of scores between the mean and a particular Z-score.Calculate the proportion of scores above or below a particular Z-score.Since the normal distribution is a continuous distribution, the probability that X is greater than or less than a particular value can be found.Ī normal curve table gives the precise percentage of scores between the mean (Z-score = 0) and any other Z score. 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. Every score in a normally distributed data set has an equivalent score in the standard normal distribution.The standard normal distribution (graph below) is a mathematical-or theoretical distribution that is frequently used by researchers to assess whether the distributions of the variables they are studying approximately follow a normal curve.Each data set or distribution of scores will have their own mean, standard deviation and shape - even when they follow a normal distribution.Ī normal distribution with a mean of 0 (u=0) and a standard deviation of 1 (o= 1) is known a standard normal distribution or a Z-distribution. Normal distributions do not necessarily have the same means and standard deviations.
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