Converting to Percentiles and Back (3 of 4)
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.