Download Test 3

Prestatistics
Review #3
Find the square root.
1) 144
A) 72
2) - 625
A) -312
3)
0.25
A) 0.005
B) -12
C) 12
D) Not a real number
B) 25
C) -25
D) Not a real number
B) 0.05
C) 5
D) 0.5
B) 81
C) 27
D) ±9
B) 19
C) 49
D) ±7
B) 4
C) -2
D) Not real number
Find the cube root.
4)
3
729
A) 9
5)
3
-343
A) -7
Find the root.
4
6) - 16
A) 2.497
Find the root. Assume that all variables represent positive numbers.
3
7) x12
A) x4
B) x6
Use the product rule to simplify the radical.
8) 75
A) 5 3
B) 8
C)
3
x12
C) 15
D) x9
D) 3 5
Simplify the radical. Assume that all variables represent positive numbers.
9) 243y2
A) 9 3y2
10)
B) 9y2 3
C) 9y 3
D) 9 3
B) 5x2 2y
C) 5xy 2
D) 5x 2y
50x2 y
A) 5xy2 2
338
x2
11)
338
x
A)
B)
13 2
x
C)
26
x
338
x2
D)
Simplify the radical.
3
12) 648
A) 18
13)
3
C) 6
3
3
D) 6
C) 1024
D) 4
3
18
2048
A) 8
14)
B) 6
3
4
B) 3
11
2048
3 108
8
3
A)
108
2
B)
Add or subtract as indicated.
15) -4 3 + 6 3
A) -24 6
3 108
8
C)
3
3
4
2
D)
3 12
2 2
B) 2 3
C) 2 6
D) -10 3
16) 22 5 - 13 5
A) 35 5
B) 45
C) 9 5
D) 9
17) 5 2 + 4 - 14 2
A) 4 + 9 2
B) 4 - 9 2
C) -5 2
D) 4 + 19 2
Add or subtract by first simplifying each radical and then combining any like radicals. Assume that all variables
represent positive numbers.
18) 7 3 - 2 75
A) 5 3
B) -17 3
C) 3 3
D) -3 3
19) 2 45 - 3 180
A) 24 5
B) 12 5
C) -24 5
D) -12 5
20) -5 128 - 6 32 - 3 200
A) -746 2
B) -5 2
C) -94 2
D) 746 2
Simplify the expression. Assume all variables represent positive real numbers.
3
21) 5x2 - 648 + 320x2
A) 9x 5 - 6
3
3
B) 8x 5 - 6
3
3
3
C) 9 5x2 - 648
D) 9x 5 - 6 18
Solve the problem.
22) Find the area of a rectangle whose length is 7 2 meters and width is 8 20 meters.
B) 112 20 sq. m
C) 224 10 sq. m
A) 112 10 sq. m
D) 56 40 sq. m
Divide and simplify. Assume that all variables represent positive real numbers.
140
23)
5
700
5
A)
140
5
B)
C) 2 7
D) 5
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
7
24)
2p
A) 7 2p
25)
7 2p
2p
C) 11p
D)
49 2p
2p
5
p
A)
26)
B)
5
p
B) 5 p
C)
5 p
p
D)
25 p
p
B) 1
C)
5x
5x
D)
5x
25x2
1
5x
A)
5x
Solve the problem by applying the Fundamental Counting Principle with two groups of items.
27) In how many ways can a girl choose a two-piece outfit from 5 blouses and 6 skirts?
A) 60
B) 13
C) 30
D) 11
28) A restaurant offers a choice of 4 salads, 5 main courses, and 4 desserts. How many possible 3-course meals are
there?
A) 160
B) 80
C) 13
D) 20
29) There are 5 roads leading from Bluffton to Hardeeville, 10 roads leading from Hardeeville to Savannah, and 3
roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon?
A) 50
B) 300
C) 18
D) 150
30) An apartment complex offers apartments with four different options, designated by A through D.
A = number of bedrooms (one through four)
B = number of bathrooms (one through three)
C = floor (first through fifth)
D = outdoor additions (balcony or no balcony)
How many apartment options are available?
A) 120
B) 240
C) 14
D) 16
31) You are taking a multiple-choice test that has 7 questions. Each of the questions has 5 choices, with one correct
choice per question. If you select one of these options per question and leave nothing blank, in how many
ways can you answer the questions?
A) 78,125
B) 16,807
C) 35
D) 12
32) License plates in a particular state display 2 letters followed by 2 numbers. How many different license plates
can be manufactured? (Repetitions are allowed.)
A) 260
B) 67,600
C) 36
D) 4
33) How many different four-letter secret codes can be formed if the first letter must be an S or a T?
A) 456,976
B) 421,824
C) 72
D) 35,152
34) Jamie is joining a music club. As part of her 4-CD introductory package, she can choose from 12 rock
selections, 10 alternative selections, 7 country selections and 5 classical selections. If Jamie chooses one selection
from each category, how many ways can she choose her introductory package?
Evaluate the factorial expression.
700!
35)
699!
A) 699
B) 700
C) 1
D) 489,300
36) 7! - 4!
A) 3
B) 5036
C) 6
D) 5016
37) (9 - 5)!
A) 4
B) 362,760
C) 362,875
D) 24
B) 24
C) 6
D) 79,833,600
B) 30
C) 15
D) 48
C) 1
D) 40
38)
12
!
3
A) 144
39)
6!
(6 - 2)!
A) 360
Use the formula for nPr to evaluate the expression.
40) 4 P0
A) 24
B) 0
Use the formula for nPr to solve.
41) A church has 10 bells in its bell tower. Before each church service 3 bells are rung in sequence. No bell is rung
more than once. How many sequences are there?
A) 1,209,600
B) 720
C) 120
D) 604,800
42) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if
there are 13 members and any member can be elected to each position? No person can hold more than one
office.
A) 1716
B) 572
C) 858
D) 17,160
43) In a contest in which 8 contestants are entered, in how many ways can the 5 distinct prizes be awarded?
A) 112
B) 672
C) 6720
D) 336
44) How many arrangements can be made using 2 letters of the word HYPERBOLAS if no letter is to be used more
than once?
A) 45
B) 90
C) 3,628,800
D) 1,814,400
Solve the problem.
45) In how many distinct ways can the letters in MANAGEMENT be arranged?
A) 226,800
B) 453,600
C) 3,628,800
46) In how many distinct ways can the letters in IMMUNOLOGY be arranged?
A) 907,200
B) 90,720
C) 1,814,400
D) 22,680
D) 3,628,800
47) A signal can be formed by running different colored flags up a pole, one above the other. Find the number of
different signals consisting of 7 flags that can be made if 4 of the flags are white, 2 are red, and 1 is blue.
A) 8
B) 105
C) 35
D) 14
48) In how many distinct ways can a 12-digit number be made using three 9ʹs and nine 3ʹs?
A) 12
B) 16
C) 8
D) 220
49) In how many distinct ways can a 9-digit number be made using four 5ʹs and five 4ʹs?
A) 126
B) 16
C) 8
D) 9
In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is not
necessary to solve the problem.
50) A record club offers a choice of 7 records from a list of 45. In how many ways can a member make a selection?
A) Permutations, because the order of the records selected does matter.
B) Combinations, because the order of the records selected does not matter.
51) One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is
$100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded?
A) Permutations, because the order of the prizes awarded matters.
B) Combinations, because the order of the prizes awarded does not matter.
52) One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is
$100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded?
A) Combinations, because the order of the prizes awarded does not matter.
B) Permutations, because the order of the prizes awarded matters.
53) How many different user IDʹs can be formed from the letters W, X, Y, Z if no repetition of letters is allowed?
A) Permutations, because the order of the letters matters.
B) Combinations, because the order of the letters does not matter.
54) Five of a sample of 100 computers will be selected and tested. How many ways are there to make this
selection?
A) Combinations, because the order of the computers selected does not matter.
B) Permutations, because the order of the computers selected does matter.
Use the formula for nCr to evaluate the expression.
55) 5 C4
A) 5
B) 20
C) 4
D) 120
56) 5 C5
A) 30
B) 120
C) 0.5
D) 1
Solve the problem.
57) From 10 names on a ballot, a committee of 4 will be elected to attend a political national convention. How
many different committees are possible?
A) 151,200
B) 210
C) 5040
D) 2520
58) In how many ways can a committee of three men and four women be formed from a group of 11 men and 11
women?
A) 554,400
B) 7,840,800
C) 54,450
D) 110
59) A physics exam consists of 9 multiple-choice questions and 6 open-ended problems in which all work must be
shown. If an examinee must answer 5 of the multiple-choice questions and 2 of the open-ended problems, in
how many ways can the questions and problems be chosen?
A) 261,273,600
B) 540
C) 453,600
D) 1890
Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest
terms.
60) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 7.
7
A) 7
B) 0
C) 1
D)
6
61) You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.
3
3
1
3
A)
B)
C)
D)
13
26
13
52
62) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1),
(2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1),
(5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two
numbers whose sum is greater than 10.
1
5
1
B) 3
C)
D)
A)
18
18
12
63) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on
any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that
the arrow will land on 3 or 4.
A) 1
B)
4
3
C) 3
D)
2
5
64) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on
any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that
the arrow will land on an odd number.
A) 0
B)
2
5
C) 1
D)
3
5
Solve the problem involving probabilities with independent events.
65) You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is shuffled, and you
draw again. Find the probability of getting a picture card the first time and a club the second time.
1
3
1
3
B)
C)
D)
A)
4
52
13
13
Solve the problem that involves probabilities with events that are not mutually exclusive.
66) Consider a political discussion group consisting of 3 Democrats, 4 Republicans, and 6 Independents. Suppose
that two group members are randomly selected, in succession, to attend a political convention. Find the
probability of selecting an Independent and then a Democrat.
1
1
18
3
A)
B)
C)
D)
52
26
169
26
Solve the problem.
67) Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1
through 6, and 2 yellow disks numbered 7 through 8, find the probability of selecting a red disk, given that an
odd-numbered disk is selected.
3
1
3
1
B)
C)
D)
A)
8
4
4
8
68) The table shows the number of employed and unemployed workers in the U.S., in thousands, in 2000.
Male
Female
Employed
67,761
58,655
Unemployed
2433
2285
Assume that one person will be randomly selected from the group described in the table. Find the probability
of selecting a person who is employed, given that the person is male.
2433
67,761
2285
2433
B)
C)
D)
A)
67,761
70,194
70,194
70,194
The exercise presents numerical information. Describe the population whose properties are analyzed by the data.
69) During 2001, there were 574 crimes in a certain city per 100,000 residents.
A) criminals in the country
B) criminals in the city
C) residents of the country
D) residents of the city
Solve the problem.
70) A recent survey revealed that 92% of computer owners in a certain city have access to the Internet. Describe the
population this statement is referring to.
71) The government of a town needs to determine if the cityʹs residents will support the construction of a new
town hall. The government decides to conduct a survey of a sample of the cityʹs residents. Which one of the
following procedures would be most appropriate for obtaining a sample of the townʹs residents?
A) Survey the first 200 people listed in the townʹs telephone directory.
B) Survey a random sample of employees at the old city hall.
C) Survey a random sample of persons within each geographic region of the city.
D) Survey every 6th person who walks into city hall on a given day.
72) The ages of 30 swimmers who participated in a swim meet are as follows:
19, 37, 31, 34, 41, 19, 51, 60, 20, 44, 52, 20, 27, 29, 42, 21, 30, 21, 59, 50, 25, 38, 47, 54, 34, 23, 23, 42, 31, 50
Construct a grouped frequency distribution for the data. Use the classes 19 - 28, 29 - 38, 39 - 48, 49 - 58, 59 - 68.
73) Construct a histogram and a frequency polygon for the given data.
Years of Education
Beyond High School
1
2
3
4
5
6
Number of People (thousands)
23
13
12
14
4
2
74) The stem-and-leaf plot below displays the ages of 30 attorneys at a small law firm.
Stems Attorneys
2
99
3
00112589
4
1234458
5
1233458
6
0137
7
12
What is the age of the oldest attorney? What is the age of the youngest attorney?
A) The oldest attorney is 62 years old. The youngest attorney is 39 years old.
B) The oldest attorney is 82 years old. The youngest attorney is 11 years old.
C) The oldest attorney is 71 years old. The youngest attorney is 28 years old.
D) The oldest attorney is 72 years old. The youngest attorney is 29 years old.
75) Which one of the following is true according to the graph?
A) If the sample is truly representative, then for a group of 50 people, we can expect about 32 of them to have
one year of education beyond high school.
B) More people had 4 years of education beyond high school than 3 years.
C) The percent of people with years of higher education greater than those shown by any rectangular bar is
equal to the percent of people with years of education less than those shown by that bar.
D) The graph is based on a sample of approximately 62 thousand people.
Describe the error in the visual display shown.
76)
The volume of our sales has doubled!!!
A) The length of a side has doubled, but the area has been multiplied by 4.
B) There is no error.
C) The length of a side has doubled, but the area has been unchanged.
D) The length of a side has doubled, but the area has been multiplied by 8.
Find the mean for the group of data items. Round to the nearest hundredth, if necessary.
77) 8, 5, 4, 11, 6, 12, 9, 4
A) 6.88
B) 8.43
C) 7.38
D) 7.86
Find the mean for the data items in the given frequency distribution. Round to the nearest hundredth, if necessary.
78)
Score
Frequency
x
f
1
5
2
2
3
1
4
6
5
7
6
10
7
9
8
12
9
11
10
11
A) 5.41
B) 6.74
C) 6.17
D) 8.1
Solve the problem.
79) Six people from different occupations were interviewed for a survey, and their annual salaries were as
follows: $12,000, $20,000, $25,000, $37,000, $67,500 and $125,000. What is the mean annual salary for the six
people?
Find the mode for the group of data items.If there is no mode, so state.
80) 11, 6, 5, 0, 2, 1, 2
A) 6
B) no mode
C) 11
81) 97, 97, 94, 57, 80, 97
A) 97
B) no mode
Find the midrange for the group of data items.
82) 12, 7, 4, 7, 2, 4, 2
A) 4.5
B) 8
83) 1.3, 2.4, 1.5, 2.6, 1.3, 2.4, 1.3, 9, 9, 1.8
A) 1.85
B) 1.95
D) 2
C) 57
D) 94
C) 7
D) 9.5
C) 5.15
D) 5.25
For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange.
84) A company advertised that, on the average, 95% of their customers reported ʺvery high satisfactionʺ with their
services. The actual percentages reported in 15 samples were the following:
95, 95, 92, 57, 71, 95, 92, 71, 95, 95, 57, 92, 92, 95, 57
a. Find the mean, median, mode and midrange. b. Which measure of central tendency was given in the
advertisement? c. Which measure of central tendency is the best indicator of the ʺaverageʺ in this situation?
A) a. mean = 83.4, median = 92, mode = 95, midrange = 76
b. mode
c. mean
B) a. mean = 83.4, median = 92, mode = 95, midrange = 76
b. mode
c. mode
C) a. mean = 83.4, median = 92, mode = 95, midrange = 76
b. mode
c. median
D) a. mean = 83.4, median = 92, mode = 95, midrange = 76
b. median
c. mean
Find the range for the group of data items.
85) 11, 12, 13, 14, 15
A) 11
B) 4
86) 11, 11, 11, 19, 23, 23, 23
A) 19
B) 8
C) 13
D) 15
C) 34
D) 12
Find a. the mean b. the deviation from the mean for each data item: and c. the sum of the deviations in part b.
87) 155, 162, 164, 169, 170
A) a. 164 b. -9, -2, 0, 5, 6 c. 0
B) a. 164 b. -9, -2, 0, 5, 6 c. 22
C) a. 162 b. -9, -2, 0, 5, 6 c. 0
D) a. 164 b. -9, -2, 0, 5, 6 c. 11
Find the standard deviation for the group of data items (to the nearest hundredth).
88) 15, 16, 17, 18, 19
A) 1.58
B) 0
C) 1.25
89) 7, 7, 7, 10, 13, 13, 13
A) 8.14
B) 9
C) 2.85
D) 2.5
D) 3
Compute the mean, range, and standard deviation for the data items in each of the three samples. Then name one way in
which the samples are alike and one way in which they are different.
90) Sample A: 12, 14, 16, 18, 20, 22, 24
Sample B: 12, 15, 15, 18, 21, 21, 24
Sample C: 12, 12, 12, 18, 24, 24, 24
A) Mean (for A, B and C): 18 Range (for A, B, and C): 12 Standard deviation: (A) 4.32 (B) 4.24 (C) 6. Samples
have the same mean but different standard deviations.
B) Mean (A) 14 (B) 15 (C) 16. Range (for A, B, and C): 12 Standard deviation: (A) 6 (B) 6 (C) 6. Samples have
the same standard deviation but different means.
C) Mean (for A, B and C): 18 Range (for A, B, and C): 12 Standard deviation: (A) 7 (B) 4.24 (C) 6. Samples
have the same mean but different standard deviations.
D) Mean (A) 17 (B) 18 (C) 19. Range (for A, B, and C): 12 Standard deviation: (A) 6 (B) 6 (C) 6. Samples have
the same standard deviation but different means.
Find the a. mean and b. standard deviation for the data set. Round to two decimal places.
91)
Country
Number of Television Sets per 100 people
A
66
B
36
C
71
D
51
E
56
A) a. 55 b. 13.69
B) a. 57 b. 13.69
C) a. 56 b. 13.69
92) International Travel Destinations of U.S. Citizens in 2000.
Country
U.S. Citizens, in thousands
A
982
B
582
C
202
D
182
E
142
F
87
G
85
H
84
I
72
J
62
A) a. 248 b. 9000
B) a. 248 b. 300.55
C) a. 242 b. 9000
D) a. 56 b. 169
D) a. 242 b. 300.55
Answer Key
Testname: PRESTAT REVIEW 3 NEW
1) C
2) C
3) D
4) A
5) A
6) C
7) A
8) A
9) C
10) D
11) B
12) C
13) A
14) C
15) B
16) C
17) B
18) D
19) D
20) C
21) A
22) A
23) C
24) B
25) C
26) C
27) C
28) B
29) D
30) A
31) A
32) B
33) D
34) 4200
35) B
36) D
37) D
38) B
39) B
40) C
41) B
42) A
43) C
44) B
45) A
46) A
47) B
48) D
49) A
50) B
51) A
Answer Key
Testname: PRESTAT REVIEW 3 NEW
52) B
53) A
54) A
55) A
56) D
57) B
58) C
59) D
60) B
61) B
62) A
63) D
64) D
65) C
66) A
67) D
68) C
69) D
70) The population is the set containing all computer owners in the city.
71) C
Age Number of Swimmers
19 - 28
10
8
72) 29 - 38
39 - 48
5
49 - 58
5
59 - 68
2
73)
74) D
75) B
76) A
77) C
78) B
Answer Key
Testname: PRESTAT REVIEW 3 NEW
79) $47,750
80) D
81) A
82) C
83) C
84) A
85) B
86) D
87) A
88) A
89) D
90) A
91) C
92) B