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

188 CHAPTER 6 | Probability
DEMONSTRATION 6.1
FINDING PROBABILITY FROM THE UNIT NORMAL TABLE
A population is normally distributed with a mean of μ = 45 and a standard deviation of
σ = 4. What is the probability of randomly selecting a score that is greater than 43? In other
words, what proportion of the distribution consists of scores greater than 43?
STEP 1
STEP 2
Sketch the distribution. For this demonstration, the distribution is normal with μ = 45
and σ = 4. The score of X = 43 is lower than the mean and therefore is placed to the left of
the mean. The question asks for the proportion corresponding to scores greater than 43, so
shade in the area to the right of this score. Figure 6.22 shows the sketch.
Transform the X value to a z-score.
z 5 X 2m
s
5
43 2 45
4
5 2 2
4 520.5
STEP 3
Find the appropriate proportion in the unit normal table. Ignoring the negative size,
locate z = –0.50 in column A. In this case, the proportion we want corresponds to the body
of the distribution and the value is found in column B. For this example,
p(X > 43) = p(z > –0.50) = 0.6915
DEMONSTRATION 6.2
PROBABILITY AND THE BINOMIAL DISTRIBUTION
Suppose that you completely forgot to study for a quiz and now must guess on every question.
It is a true/false quiz with n = 40 questions. What is the probability that you will get at
least 26 questions correct just by chance? Stated in symbols,
p(X $ 26) = ?
STEP 1
Identify p and q. This problem is a binomial situation, in which
p = probability of guessing correctly = 0.50
q = probability of guessing incorrectly = 0.50
With n = 40 quiz items, both pn and qn are greater than 10. Thus, the criteria for the normal
approximation to the binomial distribution are satisfied:
pn = 0.50(40) = 20
qn = 0.50(40) = 20
FIGURE 6.22
The distribution for
Demonstration 6.1.
43
m
45
s 5 4