211
5.4 Binomial Probability Distribution
outcomes involving two purchases; that is, the number of ways of obtaining x 5 2
successes in the n 5 3 trials. From equation (5.6) we have
n
x
3
5
2
3!
5
(3)(2)(1)
6
2!(3 2 2)! 5 (2)(1)(1) 5 2 5 3
Equation (5.6)
189
Supplementary Exercises
A large consumer goods company ran a television advertisement for one of its soap prod-ucts.
On the basis of a survey that was conducted, probabilities were assigned to the following events.
B 5 individual purchased the product
190
Chapter 4
Introduction to Probability
A survey showed that 8% of Internet users age 18 and older report keeping a blog. Refer-ring
to the 1829 age group as young adults, the survey showed that for bloggers 54% are
young adults and for nonbloggers 24%
188
Chapter 4
Introduction to Probability
What is the probability of a household having income below $25,000?
What is the probability of a household headed by someone with a bachelors degree
earning less than $25,000?
Is household income independent of ed
200
Chapter 5
Discrete Probability Distributions
As another example, consider the random variable x with the following
discrete proba-bility distribution.
x
f (x)
1
1/10
2
2/10
3
3/10
4
4/10
This probability distribution can be defined by the formula
x
f
244
Chapter 6
Continuous Probability Distributions
To illustrate how to make the third type of probability computation, suppose
we want to compute the probability of obtaining a z value of at least 1.58; that is,
P(z 1.58). The value in the z 1.5 row and
216
Chapter 5
Discrete Probability Distributions
Exercises
Methods
SELF test
25. Consider a binomial experiment with two trials and p 5 .4.
a.
Draw a tree diagram for this experiment (see Figure 5.3).
b.
Compute the probability of one success, f (1).
c.
C
239
6.2 Normal Probability Distribution
FIGURE 6.3 BELL-SHAPED CURVE FOR THE NORMAL DISTRIBUTION
Standard Deviation s
x
Mean
The normal curve has two parameters, and . They determine the location and shape of
the normal distribution.
standard
deviation
3.
Appendix 6.2 Continuous Probability Distributions with Excel
263
For continuous probability distributions, Minitab gives a cumulative
probability; that is, Minitab gives the probability that the random variable will
assume a value less than or equal to a
175
4.4 Conditional Probability
daily subscription also subscribes to the Sunday edition (event S) is .75; that is, P(S D) 5 .75.
What is the probability that a household subscribes to both the Sunday and daily editions of
the newspaper? Using the multipl
198
Chapter 5
Discrete Probability Distributions
probabilities to experimental outcomes presented in Chapter
4.
These
conditions
are the
analogs to
the two basic
requirements
for assigning
x is a
discrete
random
variable
that can
assume
the values
0, 1, 2
202
Chapter 5
Discrete Probability Distributions
What is the probability a service call will take three hours?
A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M.
and service technicians usually get off at 5:00 P.M. Wh
201
5.2 Discrete Probability Distributions
Nationally, 38% of fourth-graders cannot read an age-appropriate book. The following data
show the number of children, by age, identified as learning disabled under special
education. Most of these children have
205
5.3 Expected Value and Variance
Applications
The number of students taking the Scholastic Aptitude Test (SAT) has risen to an all-time high
of more than 1.5 million (College Board, August 26, 2008). Students are allowed to
repeat the test in hopes of
210
Chapter 5 Discrete Probability Distributions
FIGURE 5.3
TREE DIAGRAM FOR THE MARTIN CLOTHING STORE PROBLEM
First
Second
Third
Experimental
Customer
Customer
Customer
Outcome
Value of x
S
(S, S, S)
3
F
(S, S, F)
2
S
(S, F, S)
2
F
(S, F, F)
1
S
(F, S, S
234
Chapter 6
Continuous Probability Distributions
In the preceding chapter we discussed discrete random variables and their
probability dis-tributions. In this chapter we turn to the study of continuous
random variables. Specifi-cally, we discuss three c
260
Chapter 6
Continuous Probability Distributions
Is lack of sleep causing traffic fatalities? A study conducted under the auspices of the National Highway
Traffic Safety Administration found that the average number of fatal crashes caused by drowsy
driv
169
4.3 Some Basic Relationships of Probability
Exercises
Methods
22. Suppose that we have a sample space with five equally likely experimental outcomes:
E1, E2, E3, E4, E5. Let
5 cfw_E1, E2
5 cfw_E3, E4
5 cfw_E2, E3, E5
Find P(A), P(B), and P(C ).
Find P
171
4.4 Conditional Probability
For the 2375 students admitted to Penn, what is the probability that a randomly se-lected
student was accepted during early admission?
Suppose a student applies to Penn for early admission. What is the probability the
stude
172
Chapter 4
Introduction to Probability
TABLE 4.5 JOINT PROBABILITY TABLE FOR PROMOTIONS
Joint probabilities
appear in the body
Men (M )
Women (W )
Promoted (A)
.24
.03
.27
Not Promoted (Ac)
.56
.17
.73
.80
.20
1.00
of the table.
Total
Total
Marginal pr
165
4.3 Some Basic Relationships of Probability
FIGURE 4.4 COMPLEMENT OF EVENT A IS SHADED
Sample Space S
Event A
Ac
Complement
of Event A
Solving for P(A), we obtain the following result.
COMPUTING PROBABILITY USING THE COMPLEMENT
P(A) 5 1 2 P(Ac )
(4.5)
174
Chapter 4
Introduction to Probability
We already determined that P(A M ) 5 .30. Let us now use the probability
values in Table 4.5 and the basic relationship of conditional probability in
equation (4.7) to compute the probability that an officer is pr
176
Chapter 4
Introduction to Probability
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we
know P(A) 5 .30 and P(B) 5 .40.
What is P(A B)?
What is P(A B)?
A student in statistics argues that the concepts of mutu
178
Chapter 4
Introduction to Probability
Late in a basketball game, a team often intentionally fouls an opposing player in or-der
to stop the game clock. The usual strategy is to intentionally foul the other teams
worst free-throw shooter. Assume that th
173
4.4 Conditional Probability
A and M; that is, P(A M ) 5 .24. Also note that .80 is the marginal probability that
a ran-domly selected officer is a man; that is, P(M ) 5 .80. Thus, the conditional
probability P(A M ) can be computed as the ratio of the
197
5.2 Discrete Probability Distributions
Consider the experiment of a worker assembling a product.
Define a random variable that represents the time in minutes required to assemble the
product.
What values may the random variable assume?
Is the random v
235
6.1 Uniform Probability Distribution
FIGURE 6.1 UNIFORM PROBABILITY DISTRIBUTION FOR FLIGHT TIME
f (x)
1
20
x
120
125
130
135
140
Flight Time in Minutes
As noted in the introduction, for a continuous random variable, we consider
proba-bility only in t
191
Case Problem Hamilton County Judges
TABLE 4.8 TOTAL CASES DISPOSED, APPEALED, AND REVERSED IN HAMILTON
COUNTY COURTS
Common Pleas Court
Judge
WEB file
Judge
Total Cases
Appealed
Reversed
Disposed
Cases
Cases
Fred Cartolano
3,037
137
12
Thomas Crush
3,
248
Chapter 6
Continuous Probability Distributions
Again, we see the important role that probability distributions play in providing decisionmaking information. Namely, once a probability distribution is established for a particular application, it can be
240
Chapter 6
Continuous Probability Distributions
The normal distribution is symmetric, with the shape of the normal curve to
the left of the mean a mirror image of the shape of the normal curve to the
right of the mean. The tails of the normal curve ext