http://www.ck12.org Chapter 5. Normal Distribution
distributed normally, then az−score can tell us something about how our test score relates to the rest of the class.
From the empirical rule we know that about 68 percent of the students would have scored between az−score of− 1
and 1, or between a 75 and an 89. If 68% of the data is between those two values, then that leaves a remaining 32%
in the tail areas. Because of symmetry, that leaves 16% in each individual tail.
If we combine the two percentages, approximately 84% of the data is below an 89 score. We typically refer to this
as apercentile. A student with this score could conclude that he or she performed better than 84% of the class, and
that he or she was in the 84thpercentile.
This same conclusion can be put in terms of a probability distribution as well. We could say that if a student from
this class were chosen at random the probability that we would choose a student with a score of 89 or less is.84, or
there is an 84% chance of picking such a student.