Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

178 CHAPTER 6 | Probability
BOX 6.1 Probabilities, Proportions, and Percentile Ranks
Thus far we have discussed parts of distributions in
terms of proportions and probabilities. However, there
is another set of terminology that deals with many of the
same concepts. Specifically, in Chapter 2 we defined the
percentile rank for a specific score as the percentage of
the individuals in the distribution who have scores that
are less than or equal to the specific score. For example,
if 70% of the individuals have scores of X = 45 or
lower, then X = 45 has a percentile rank of 70%. When
a score is referred to by its percentile rank, the score is
called a percentile. For example, a score with a percentile
rank of 70% is called the 70th percentile.
Using this terminology, it is possible to rephrase
some of the probability problems that we have
been working. In Example 6.6, the problem was
presented as “What is the probability of randomly
selecting an individual with an IQ of less than
120?” Exactly the same question could be phrased
as “What is the percentile rank for an IQ score of
120?” In each case, we are looking for the proportion
of the distribution corresponding to scores
equal to or less than 120. Similarly, Example 6.10
asked “How much time do you have to spend commuting
each day to be in the highest 10% nationwide?”
Because this score separates the top 10%
from the bottom 90%, the same question could be
rephrased as “What is the 90th percentile for the
distribution of commuting times?”
LEARNING CHECK
1. For a normal distribution with a mean of μ = 500 and σ = 100, what is the probability
of selecting an individual with a score less than 400?
a. 0.1587
b. 0.8413
c. 0.34.13
d. –0.15.87
2. For a normal distribution with a mean of μ = 40 and σ = 4, what is the probability
of selecting an individual with a score greater than 46?
a. 0.0668
b. 0.4452
c. 0.9332
d. 0.0548
3. SAT scores for a normal distribution with mean of μ = 500 with σ = 100. What
SAT score separates the top 10% of the distribution from the rest?
a. 128
b. 628
c. 501.28
d. 372
ANSWERS
1. A, 2. A, 3. B