Converting to Percentiles and Back (4 of 4)
Next section: Area under portions
of the curve
What score on the Introductory Psychology test would it have taken to
be in the 75th percentile? (Remember the test has a mean of 80 and a
standard deviation of 5.) The answer is computed by reversing the steps in
the previous problems.
First, determine how many standard deviations
above the mean one would have to be to be in the 75th percentile.
This can be found by using a z table and finding the z associated
with 0.75. The value of z is 0.674. Thus, one must be .674 standard
deviations above the mean to be in the 75th percentile.
Second, the
standard deviation is 5, one must be:
(5)(.674) = 3.37
points above
the mean. Since the mean is 80, a score of 80 + 3.37 = 83.37 is
necessary. Rounding off, a score of 83 is needed to be in the 75th
percentile. Since
,
X = 80 + (.674)(5) = 83.37 as just shown in the figure.
Next section: Area under portions of the curve