Converting to Percentiles and Back (3 of 4)

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When z is negative it means that X is below the mean. Thus, a z of -2 means that X is -2 standard deviations above the mean which is the same thing as being +2 standard deviations below the mean.

To take another example, what is the percentile rank of a person receiving a score of 90 on the test?



The graph shows that most people scored below 90. Since 90 is 2 standard deviations above the mean

z = (90 - 80)/5 = 2

it can be determined from the table that a z score of 2 is equivalent to the 97.7th percentile: The proportion of people scoring below 90 is thus .977.