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Chapter 6 Chapter 7 Chapter 8 Chapter 9
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A sample of 1000 women was polled; the women were asked the question
“How often during the week do you serve a vegetarian (meatless) main
dish to your family at dinnertime?” Partial results follow.
What is the probability that a woman never serves her family a vegetarian
main dish at dinnertime?
A) 0.65
B) 0
C) 0.35
C
Suppose we have a “loaded” (unfair) die that gives the
outcomes 1 through 6 according to the following probability
distribution.
If this die is rolled 6000 times, the number of times we get
either a 2 or a 3 should be about
A) 1000
B) 2000
C) 3000
C
Students at X University must be in one of four class
ranks: freshman, sophomore, junior, or senior. At
this university, 35% of the students are freshmen and
30% are sophomores. If a student is chosen at
random, the probability that he or she is either a
junior or a senior is
A) 35%
B) 65%
C) 70%
A
Suppose we toss a fair penny and a fair nickel. Let A
be the event that the penny lands heads and B be the
event that the nickel lands tails. The events A and B
are
A) Disjoint
B) Independent
C) Complements
B
In the wild, 400 randomly selected blooming azalea
plants are observed and classified according to
flower petal color (white, pink, or orange) and
whether or not they have a fragrance. The table gives
the results.
If a single azalea plant is selected at random, the
probability that it has pink flower petals or no
fragrance is
A) 0.04
B) 0.635
C) 0.595
C
Suppose that we have a deck of three cards, one
marked with a 1, one marked with a 2, and one
marked with a 5. You draw two cards at random and
without replacement from the deck. The sample
space S = {(1, 2), (1, 5), (2, 5)} consists of these
three equally likely outcomes. Let X be the sum of
the numbers on the two cards drawn. Which of the
following is the correct probability distribution for
X?
A
In a particular game, a ball is randomly chosen from
a box that contains 3 red balls, 1 green ball, and 6
blue balls. If a red ball is selected, you win $2; if a
green ball is selected, you win $4; if a blue ball is
selected, you win nothing. Let X be the amount that
you win. The expected value of X is
A) $1
B) $2
C) $3
A
Let X = the number of times that a customer visits a
grocery store during a one-week period. Assume that
the probability distribution of X is as follows:
The standard deviation of X, σX, is approximately
A) 1.5
B) 0.65
C) 0.81
C
The time in minutes X that you must wait before a
train arrives at your local subway station is a
uniformly distributed random variable between 5
minutes and 15 minutes. That is, the density curve of
the distribution of x has constant height between 5
and 15 and height 0 outside this interval. Determine
P(6 < X < 8).
A) 0.1
B) 0.5
C) 0.2
C
The weight of a medium-sized orange selected at
random from a large bin of oranges at a local
supermarket is a random variable with mean μ = 12
ounces and standard deviation σ = 1.2 ounces.
Suppose we independently select two oranges at
random from the bin. The difference in the weights
of the two oranges (the weight of the first orange
minus the weight of the second orange) is a random
variable with a standard deviation equal to
A) 0
B) 1.7
C) 2.88
B
There are 20 multiple-choice questions on an exam,
each having four possible responses, of which only
one is correct. Each question is worth 5 points if
answered correctly. Suppose that a student guesses
the answer to each question, with her guesses from
question to question being independent. If the
student needs at least 40 points to pass the exam, the
probability that she passes is closest to
A) 0.0609
B) 0.1018
C) 0.9591
B
There are 20 multiple-choice questions on an exam,
each having four possible responses, of which only
one is correct. Each question is worth 5 points if
answered correctly. Suppose that a student guesses
the answer to each question, with her guesses from
question to question being independent. The
student’s expected (mean) score on this exam is
A) 25
B) 5
C) 50
A
In the gambling game of chuck-a-luck, three dice are
rolled using a rotating, hourglass-shaped cage. The
player chooses one of the 6 possible sides (1, 2, 3, 4,
5, or 6) and receives a payoff the amount of which
depends on how many dice turn up on that particular
side. Let X = the number of times the dice have to be
rolled until we see “three of a kind” (of any type).
Which of the following probability distributions does
X have?
B
In a certain large population, 70% are right-handed.
You need a left-handed pitcher for your softball team
and decide to find one by asking people chosen from
the population at random. (We assume that once you
do find a left-hander, he or she will be happy to join
your team and will not say no.) The probability that
the first left-hander you find is the fourth person you
ask is approximately
A) 0.1029
B) 0.019
C) 0.072
A
For which of the following
choices of n, p can we not use the
normal approximation to the
binomial distribution?
C
A news magazine claims that 30% of all New York
City police officers are overweight. Indignant at this
claim, the New York City police commissioner
conducts a survey in which 200 randomly selected
New York City police officers are weighed. 52, or
26%, of the surveyed officers turn out to be
overweight. Which of the following statements about
this situation is true?
A
As part of a promotion for a new type of cracker,
free samples are offered to shoppers in a local
supermarket. The probability that a shopper will buy
a package of crackers after tasting the free sample is
0.2. Different shoppers can be regarded as
independent trials. Let be the sample proportion of
the next n shoppers that buy a packet of crackers
after tasting a free sample. How large should n be so
that the standard deviation of is no more than 0.01?
A) 4
B) 16
C) 1600
C
As part of a promotion for a new type of cracker,
free samples are offered to shoppers in a local
supermarket. The probability that a shopper will buy
a package of crackers after tasting the free sample is
0.2. Different shoppers can be regarded as
independent trials. Let be the sample proportion of
the next 100 shoppers that buy a package of crackers
after tasting a free sample. The probability that fewer
than 30% of these individuals buy a package of
crackers after tasting a sample is approximately
(without using the continuity correction)
A) 0.3
B) 0.9938
C) 0.0062
B
The duration of Alzheimer’s disease, from the onset
of symptoms until death, ranges from 3 to 20 years,
with a mean of 8 years and a standard deviation of 4
years. The administrator of a large medical center
randomly selects the medical records of 30 deceased
Alzheimer’s patients and records the duration of the
disease for each one. Find the probability that the
average duration of the disease for the 30 patients
will exceed 8.25 years.
A) 0.6331
B) 0.3669
C) 0.4761
B
The duration of Alzheimer’s disease, from the onset
of symptoms until death, ranges from 3 to 20 years,
with a mean of 8 years and a standard deviation of 4
years. The administrator of a large medical center
randomly selects the medical records of 30 deceased
Alzheimer’s patients and records the duration of the
disease for each one. Find the probability that the
average duration of the disease for the 30 patients
will lie within 1 year of the overall mean of 8 years.
A) 0.8294
B) 0.1706
C) 0.4147
A
According to the "1.5 x IQR"
rule, how many outliers are there
in the data set 110, 144, 115, 123,
114, 118, 72, 156?
A) None
B) One
C) Two
B
You have a set of data that you suspect may have
come from a normal distribution. To assess
normality, you construct a normal probability plot.
Which of the following would constitute evidence
that the data did actually arise from a normal
distribution?
A
For 10 pairs of data (x, y), we obtain the following summary
statistics:
The 10 x-values have sample mean 0.30 and sample standard
deviation 0.02.
The 10 y-values have sample mean 0.28 and sample standard
deviation 0.04.
The correlation coefficient r = 0.896.
The equation of the least-squares regression line of y on x is
B
Suppose that a scatterplot of log y versus x shows a
strongly linear relationship with a value of r close
to 1. Which of the following will then occur?
B
You would like to compare the level of mathematical
knowledge among 15-year-olds in the United States
and Japan. To do this, you plan to give a
mathematics achievement test to random samples of
1000 15-year-olds in each of the two countries. To
ensure that the samples will include individuals from
all different socioeconomic groups and educational
backgrounds, you will randomly select 200 students
from low-income families, 400 students from
middle-income families, and 400 students from highincome families in each country. The sampling
procedure being used here is
A) Simple Random
B) Cluster
C) Stratified
C