Converting to Percentiles and Back (2 of 4)

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What about a person scoring 75 on the test? The proportion of the area below 75 is the same as the proportion of scores below 75.



A score of 75 is one standard deviation below the mean because the mean is 80 and the standard deviation is 5. Mathematical statisticians have determined that 15.9% of the scores in a normal distribution are lower than a score one standard deviation below the mean. Therefore, the proportion of the scores below 75 is 0.159 and a person scoring 75 would have a percentile rank score of 15.9.
The table below page gives the proportion of the scores below various values of z; z is computed with the formula:



where z is the number of standard deviations (σ) X is above the mean (μ).

Naturally, it is more conventient to use a z calculator.