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

PROBLEMS 189
FIGURE 6.23
The normal approximation
of a binomial distribution
with μ = 20 and σ = 3.16.
The proportion corresponding
to scores that are equal
to or greater than 26 is
shaded. Notice that the
lower real limit (25.5) for
X = 26 is used.
m
20
s 5 3.16
25.5
X
STEP 2
STEP 3
Identify the parameters, and sketch the binomial distribution. For a true/false quiz, correct
and incorrect guesses are equally likely, p = q = 1 2 . With pn and qn both greater than 10, the
normal approximation is appropriate and will have a mean and a standard deviation as follows:
m5pn 5 0.5(40) 5 20
s5Ïnpq 5 Ï10 5 3.16
Figure 6.23 shows the distribution. We are looking for the probability of getting X = 26 or
more questions correct, so we will use the lower real limit for 26, which is 25.5.
The z-score for X = 25.5 is calculated as follows:
z 5 X 2 pn
Ïnpq
5
25.5 2 20
3.16
511.74
According to the unit normal table, the proportion we want is 0.0409. Thus, the probability
of getting at least 26 questions right just by guessing is
p(X $ 26) = 0.0409 (or 4.09%)
PROBLEMS
1. What are the two requirements for a random sample?
2. Define sampling with replacement and explain why is
it used?
3. Around Halloween each year the grocery store sells
three-pound bags of candy contains a mixture of three
different mini-bars: Snickers, Milky Way, and Twix.
If the bag has an equal number of each of the three
bars, then what are the probabilities for each of the
following?
a. Randomly selecting a Milky Way bar.
b. Randomly selecting either a Snickers or
Twix bar.
c. Randomly selecting something other than a Twix
bar.
4. A psychology class consists of 28 males and 52 females.
If the professor selects names from the class list using
random sampling,
a. What is the probability that the first student
selected will be a female?
b. If a random sample of n = 3 students is selected and
the first two are both females, what is the probability
that the third student selected will be a male?
5. Draw a vertical line through a normal distribution for
each of the following z-score locations. Determine
whether the tail is on the right or left side of the line
and find the proportion in the tail.
a. z = 1.00
b. z = 0.50
c. z = –1.25
d. z = –0.40