statistics
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Chapter 1..
1.1 The following measurements were recorded for
the drying time, in hours, of a certain brand of latex
paint.
3.4 2.5 4.8 2.9 3.6
2.8 3.3 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
Assume that the measurements are a simple random
sample.
(a) What is the sample size for the above sample?
(b) Calculate the sample mean for these data.
(c) Calculate the sample median.
(d) Plot the data by way of a dot plot.
(e) Compute the 20% trimmed mean for the above
data set.
(f) Is the sample mean for these data more or less descriptive
as a center of location than the trimmed
mean?
1.7 Consider the drying time data for Exercise 1.1
on page 13. Compute the sample variance and sample
standard deviation.
1.13 A manufacturer of electronic components is interested
in determining the lifetime of a certain type
of battery. A sample, in hours of life, is as follows:
123, 116, 122, 110, 175, 126, 125, 111, 118, 117.
(a) Find the sample mean and median.
(b) What feature in this data set is responsible for the
substantial difference between the two?
1.19 The following data represent the length of life in
years, measured to the nearest tenth, of 30 similar fuel
pumps:
2.0 3.0 0.3 3.3 1.3 0.4
0.2 6.0 5.5 6.5 0.2 2.3
1.5 4.0 5.9 1.8 4.7 0.7
4.5 0.3 1.5 0.5 2.5 5.0
1.0 6.0 5.6 6.0 1.2 0.2
(a) Construct a stem-and-leaf plot for the life in years
of the fuel pumps, using the digit to the left of the
decimal point as the stem for each observation.
(b) Set up a relative frequency distribution
(c) Compute the sample mean, sample range, and sample
standard deviation.
Chapter 2..
2.1 List the elements of each of the following sample
spaces:
(a) the set of integers between 1 and 50 divisible by 8;
(b) the set S = {x | x2 + 4x − 5 = 0};
(c) the set of outcomes when a coin is tossed until a
tail or three heads appear;
(d) the set S = {x | x is a continent};
(e) the set S = {x | 2x − 4 ≥ 0 and x < 1}.
2.5 An experiment consists of tossing a die and then
flipping a coin once if the number on the die is even. If
the number on the die is odd, the coin is flipped twice.
Using the notation 4H, for example, to denote the outcome
that the die comes up 4 and then the coin comes
up heads, and 3HT to denote the outcome that the die
comes up 3 followed by a head and then a tail on the
coin, construct a tree diagram to show the 18 elements
of the sample space S.
2.7 Four students are selected at random from a
chemistry class and classified as male or female. List
the elements of the sample space S1, using the letter
M for male and F for female. Define a second sample
space S2 where the elements represent the number of
females selected.
2.9 For the sample space of Exercise 2.5,
(a) list the elements corresponding to the event A that
a number less than 3 occurs on the die;
(b) list the elements corresponding to the event B that
two tails occur;
(c) list the elements corresponding to the event A’
2.14 If S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and A =
{0, 2, 4, 6, 8}, B = {1, 3, 5, 7, 9}, C = {2, 3, 4, 5}, and
D = {1, 6, 7}, list the elements of the sets corresponding
to the following events:
(a) A ∪ C;
(b) A ∩ B;
(c) C
?
;
(d) (C
? ∩ D) ∪ B;
(e) (S ∩ C)
?
;
(f) A ∩ C ∩ D
?
2.16 If S = {x | 0 < x < 12}, M = {x | 1 < x < 9},
and N = {x | 0 < x < 5}, find
(a) M ∪ N;
(b) M ∩ N;
(c) M
? ∩ N
?
.
2.17 Let A, B, and C be events relative to the sample
space S. Using Venn diagrams, shade the areas
representing the following events:
(a) (A ∩ B)
?
;
(b) (A ∪ B)
?
;
(c) (A ∩ C) ∪ B.
2.21 Registrants at a large convention are offered 6
sightseeing tours on each of 3 days. In how many
ways can a person arrange to go on a sightseeing tour
planned by this convention?
2.22 In a medical study, patients are classified in 8
ways according to whether they have blood type AB+,
AB
−
, A+, A
−
, B+, B
−
, O+, or O
−
, and also according
to whether their blood pressure is low, normal, or
high. Find the number of ways in which a patient can
be classified.
2.23 If an experiment consists of throwing a die and
then drawing a letter at random from the English
alphabet, how many points are there in the sample
space?
2.24 Students at a private liberal arts college are classified
as being freshmen, sophomores, juniors, or seniors,
and also according to whether they are male or
female. Find the total number of possible classifications
for the students of that college.
2.25 A certain brand of shoes comes in 5 different
styles, with each style available in 4 distinct colors. If
the store wishes to display pairs of these shoes showing
all of its various styles and colors, how many different
pairs will the store have on display?
2.28 A drug for the relief of asthma can be purchased
from 5 different manufacturers in liquid, tablet, or
capsule form, all of which come in regular and extra
strength. How many different ways can a doctor prescribe
the drug for a patient suffering from asthma?
2.29 In a fuel economy study, each of 3 race cars is
tested using 5 different brands of gasoline at 7 test sites
located in different regions of the country. If 2 drivers
are used in the study, and test runs are made once under
each distinct set of conditions, how many test runs
are needed?
2.33 If a multiple-choice test consists of 5 questions,
each with 4 possible answers of which only 1 is correct,
(a) in how many different ways can a student check off
one answer to each question?
(b) in how many ways can a student check off one
answer to each question and get all the answers
wrong?
2.36 (a) How many three-digit numbers can be
formed from the digits 0, 1, 2, 3, 4, 5, and 6 if
each digit can be used only once?
(b) How many of these are odd numbers?
(c) How many are greater than 330?
2.38 Four married couples have bought 8 seats in the
same row for a concert. In how many different ways
can they be seated
(a) with no restrictions?
(b) if each couple is to sit together?
(c) if all the men sit together to the right of all the
women?
2.41 Find the number of ways that 6 teachers can
be assigned to 4 sections of an introductory psychology
course if no teacher is assigned to more than one
section.
2.44 In how many ways can a caravan of 8 covered
wagons from Arizona be arranged in a circle?
2.46 In how many ways can 3 oaks, 4 pines, and 2
maples be arranged along a property line if one does
not distinguish among trees of the same kind?
2.51 A box contains 500 envelopes, of which 75 contain
$100 in cash, 150 contain $25, and 275 contain
$10. An envelope may be purchased for $25. What is
the sample space for the different amounts of money?
Assign probabilities to the sample points and then find
the probability that the first envelope purchased contains
less than $100.
2.53 The probability that an American industry will
locate in Shanghai, China, is 0.7, the probability that
it will locate in Beijing, China, is 0.4, and the probability
that it will locate in either Shanghai or Beijing or
both is 0.8. What is the probability that the industry
will locate
(a) in both cities?
(b) in neither city?
2.55 If each coded item in a catalog begins with 3
distinct letters followed by 4 distinct nonzero digits,
find the probability of randomly selecting one of these
coded items with the first letter a vowel and the last
digit even.
2.58 A pair of fair dice is tossed. Find the probability
of getting
(a) a total of 8;
(b) at most a total of 5.
2.60 If 3 books are picked at random from a shelf containing
5 novels, 3 books of poems, and a dictionary,
what is the probability that
(a) the dictionary is selected?
(b) 2 novels and 1 book of poems are selected?
2.61 In a high school graduating class of 100 students,
54 studied mathematics, 69 studied history, and
35 studied both mathematics and history. If one of
these students is selected at random, find the probability
that
(a) the student took mathematics or history;
(b) the student did not take either of these subjects;
(c) the student took history but not mathematics.
2.75 A random sample of 200 adults are classified below
by sex and their level of education attained.
Education Male Female
Elementary 38 45
Secondary 28 50
College 22 17
If a person is picked at random from this group, find
the probability that
(a) the person is a male, given that the person has a
secondary education;
(b) the person does not have a college degree, given
that the person is a female.
2.81 The probability that a married man watches a
certain television show is 0.4, and the probability that
a married woman watches the show is 0.5. The probability
that a man watches the show, given that his wife
does, is 0.7. Find the probability that
(a) a married couple watches the show;
(b) a wife watches the show, given that her husband
does;
(c) at least one member of a married couple will watch
the show.
2.83 The probability that a vehicle entering the Luray
Caverns has Canadian license plates is 0.12; the
probability that it is a camper is 0.28; and the probability
that it is a camper with Canadian license plates
is 0.09. What is the probability that
(a) a camper entering the Luray Caverns has Canadian
license plates?
(b) a vehicle with Canadian license plates entering the
Luray Caverns is a camper?
(c) a vehicle entering the Luray Caverns does not have
Canadian plates or is not a camper?
2.85 The probability that a doctor correctly diagnoses
a particular illness is 0.7. Given that the doctor
makes an incorrect diagnosis, the probability that the
patient files a lawsuit is 0.9. What is the probability
that the doctor makes an incorrect diagnosis and the
patient sues?
2.87 A real estate agent has 8 master keys to open
several new homes. Only 1 master key will open any
given house. If 40% of these homes are usually left
unlocked, what is the probability that the real estate
agent can get into a specific home if the agent selects
3 master keys at random before leaving the office?
2.91 Find the probability of randomly selecting 4
good quarts of milk in succession from a cooler containing
20 quarts of which 5 have spoiled, by using
(a) the first formula of Theorem 2.12 on page 68;
(b) the formulas of Theorem 2.6 and Rule 2.3 on pages
50 and 54, respectively.
2.95 In a certain region of the country it is known
from past experience that the probability of selecting
an adult over 40 years of age with cancer is 0.05. If
the probability of a doctor correctly diagnosing a person
with cancer as having the disease is 0.78 and the
probability of incorrectly diagnosing a person without
cancer as having the disease is 0.06, what is the probability
that an adult over 40 years of age is diagnosed
as having cancer?
2.96 Police plan to enforce speed limits by using radar
traps at four different locations within the city limits.
The radar traps at each of the locations L1, L2, L3,
and L4 will be operated 40%, 30%, 20%, and 30% of
the time. If a person who is speeding on her way to
work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively,
of passing through these locations, what is the
probability that she will receive a speeding ticket?
2.98 If the person in Exercise 2.96 received a speeding
ticket on her way to work, what is the probability
that she passed through the radar trap located at L2?
2.101 A paint-store chain produces and sells latex
and semigloss paint. Based on long-range sales, the
probability that a customer will purchase latex paint is
0.75. Of those that purchase latex paint, 60% also purchase
rollers. But only 30% of semigloss paint buyers
purchase rollers. A randomly selected buyer purchases
a roller and a can of paint. What is the probability
that the paint is latex?
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