Download Chapter 12 Review

Chapter 12 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Alan’s online test has 10 true-false questions and 5 multiple-choice questions. Each multiple-choice question
has 4 different answer choices. How many different choices for answering the 15 questions are possible?
a. 15
c. 300
b. 100
d. 1,048,576
____
2. A pizza corner offers a choice of 2 types of pizza bases and 8 types of pizza toppings. How many different
single topping pizzas can a customer order?
a. 2
c. 10
b. 8
d. 16
____
3. In a library, one copy each of 40 new books has been added to its reference section. In addition, the contents
of the books have been uploaded to the online library database. There are 4 LAN terminals in the reference
section of the library. Therefore, each of the new books can be referred to in the form of its hard copy as well
as soft copy at 4 computers. How many ways can a member choose a new book and its form to refer?
a. 40
c. 160
b. 80
d. 200
____
4. John is getting his ATM card activated. He must select a password containing 4 nonzero digits to be able to
use the card. How many passwords are allowed if no digit may be used more than once?
a. 3,024
c. 15,120
b. 5,040
d. 30,240
____
5. Tina has to create a password for the security of a software program file. She wants to use a password with 3
letters. How many passwords are allowed if no letters are repeated and the password is not case sensitive?
a. 13,800
c. 17,576
b. 15,600
d. 46,800
____
6. There are 9 children playing in a playground. In a game, they all have to stand in a line such that the youngest
child is at the beginning of the line. How many ways can the children be arranged in the line?
a. 40,320
c. 16,777,216
b. 362,880
d. 387,420,489
____
7. In how many ways can 8 different books be arranged over one another if one of the books is an encyclopedia
and it must be on the second position from the top?
a. 720
c. 5,040
b. 2,520
d. 40,320
____
8. In how many ways can 6 members of a dance group in different color costumes be made to stand in a line if
the first person is in a yellow costume?
a. 24
c. 720
b. 120
d. 3,125
There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected
for a stage performance. Find the probability of the following selection.
____
9. P(2 brown-haired children)
a.
c.
b.
d.
____ 10. P(2 black-haired children)
a.
c.
b.
d.
____ 11. P(1 brown-haired and 1 black-haired child)
a.
c.
b.
d.
Laura has moved to a new apartment. Her schoolbooks comprising of different subjects are mixed in a bag
during the move. Four books are of mathematics, three are English, and six are science. If Laura opens the
bag and selects books at random, find the given probability.
____ 12. P(1 science and 2 mathematics books)
a.
c.
b.
d.
Find the odds of an event occurring with the given the probability of the event.
____ 13.
a. 1:12
c.
b.
d. 12:1
a. 9:3
c.
b. 3:9
d.
____ 14.
Three tickets are selected at random from a box of tickets bearing numbers from 1 to 30. The table and the
relative-frequency histogram show the distribution of the number of even-numbered tickets chosen. Find the
given probability.
Tickets with Even Numbers
0
1
2
3
Probability
____ 15. P(0 even-numbered tickets)
a.
b.
____ 16. P(3 even-numbered tickets)
a.
b.
c.
d.
c.
d.
____ 17. In a basket, there are 7 male kittens and 5 female kittens. Donna randomly selects one, puts it back, and then
randomly selects another. What is the probability that both selections were female kittens?
a.
c.
b.
d.
____ 18. A bag contains 6 red, 7 blue, and 5 green coins. If 3 coins are randomly selected in succession, what is the
probability of selecting a red coin, then a blue coin, and then a green coin, if replacement occurs each time?
a.
c.
b.
d.
____ 19. What is the probability of getting a 4 each time if a die is rolled 3 times?
a.
c.
b.
d.
____ 20. The table shows the heights (in centimeters) of students of class IX.
145
155
155.5
158
160.6
165
170
175
175
175.9
180
Find the mean, median, and mode of the heights to the nearest tenth.
a. 165.0, 165.0, and 155.5
b. 165.0, 165.0, and 175.0
c. 166.5, 165.0, and 175.0
d. 165.0, 170.0, and 175.0
Determine whether the given event is mutually exclusive or inclusive. Then find the probability.
____ 21. A card is drawn from a standard deck of cards.
P(queen or jack)
a.
c.
Mutually inclusive;
Mutually exclusive;
b.
Mutually exclusive;
d.
Mutually inclusive;
____ 22. Each of the numbers from 1 to 50 is written on a tile and the tiles are placed upside down on the top of a table.
If a tile is picked up at random, what is the probability that the number on the tile is a multiple of 7 or a
multiple of 8?
a.
c.
b.
d.
A dice is rolled. What is the probability of rolling the following?
____ 23. a multiple of 2 or a multiple of 5
a.
b.
c.
d.
Find the margin of sampling error to the nearest percent.
____ 24. p = 67%, n = 500
a. 0.04%
b. 9%
c. 2%
d. 4%
____ 25. p = 16%, n = 1000
a. 0.027%
b. 0.023%
c. 12%
d. 2%
In a race, Brian Collins has to cross 10 hurdles. The probability that he clears a hurdle is
probability.
____ 26. P(clears exactly 4 hurdles)
. Find the
a.
c.
b.
d.
____ 27. P(not more than two hurdles are cleared)
a.
b.
c.
d.
Determine whether the following situation would produce a random sample. Write Yes or No and explain
your answer.
____ 28. surveying people going to a Thai restaurant to find their favorite food
a. No, the people surveyed would be probably more likely than others to prefer Thai food.
b. No, the people surveyed would be probably more likely than others to prefer Chinese
food.
c. Yes, the people surveyed would be probably more likely than other to prefer Thai food.
d. Yes, the general preference of the people going to a Thai restaurant can be used to produce
random sample.
The marks obtained by students of a class in a test are normally distributed with a mean of 60 marks and a
standard deviation of 5 marks.
____ 29. About what percent of students have scored between 55 and 65 marks?
a. 2.5
c. 47.5
b. 34
d. 68
____ 30. About what percent of students have scored less than 45 marks?
a. 0.5
c. 15.5
b. 2.5
d. 34
Chapter 12 Review
Answer Section
MULTIPLE CHOICE
1. ANS: D
By the Fundamental Counting Principle, the total number of ways in which Alan can answer the 15 questions
is 210 45
Feedback
A
B
C
D
Recalculate the ways of attempting a question.
How many possible answer choices are there in multiple-choice questions?
Have you used the Fundamental Counting Principle correctly?
Correct!
PTS: 1
DIF: Advanced
REF: Page 634
OBJ: 12-1.1 Solve problems involving independent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving independent events.
KEY: Solve Problems | Probability | Independent Events
2. ANS: D
The total number of different types of single topping pizzas a customer can order is the same as the total
number of combinations of pizza bases and toppings.
Feedback
A
B
C
D
How many different types of toppings are there to create different combinations?
How many types of pizza bases are there for making different pizzas?
What is the value of the product of the types of pizza bases and the number of toppings?
Correct!
PTS: 1
DIF: Average
REF: Page 634
OBJ: 12-1.1 Solve problems involving independent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving independent events.
KEY: Solve Problems | Probability | Independent Events
3. ANS: D
By the Fundamental Counting Principle, the number of ways a member can refer to a new book is 40 · 5
Feedback
A
B
C
D
All the 40 books are present in more than one format.
The soft copy of a book can be referred to on 4 terminals.
Have you applied the Fundamental Counting Principle correctly?
Correct!
PTS: 1
DIF: Average
REF: Page 635
OBJ: 12-1.1 Solve problems involving independent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving independent events.
KEY: Solve Problems | Probability | Independent Events
4. ANS: A
The selection of nonzero digits for a password, without repeating any digits, is a dependent event. The total
passwords allowed are 9 · 8 · 7 · 6 or 3,024.
Feedback
A
B
C
D
Correct!
How many nonzero digits are there in the password?
How many digits the required password should contain?
Only nonzero digits must be used for making 4-digit passwords.
PTS: 1
DIF: Average
REF: Page 635
OBJ: 12-1.2 Solve problems involving dependent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving dependent events.
KEY: Solve Problems | Probability | Dependent Events
5. ANS: B
According to the Fundamental Counting Principle, the total passwords allowed are 26 25 24.
Feedback
A
B
C
D
How many letters are there in the set of alphabets?
Correct!
What type of event does this selection involve?
Did you use the Fundamental Counting Principle correctly?
PTS: 1
DIF: Advanced
REF: Page 635
OBJ: 12-1.2 Solve problems involving dependent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving dependent events.
KEY: Solve Problems | Probability | Dependent Events
6. ANS: A
The selection of children for various positions in the line is a dependent event. According to the Fundamental
Counting Principle, the total number of arrangements is 40,320.
Feedback
A
B
C
D
Correct!
Recalculate the number of ways of arrangement.
What type of event do the selections for second to eight positions in the line involve?
What type of event does the arrangement of nine children in a line involve?
PTS: 1
DIF: Advanced
REF: Page 635
OBJ: 12-1.2 Solve problems involving dependent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving dependent events.
KEY: Solve Problems | Probability | Dependent Events
7. ANS: C
There is only 1 choice for the second position from the top. The remaining 7 books can be arranged in 7!
ways.
Feedback
A
B
C
D
Check the number of books that can be arranged.
What is the maximum number of choices for any position of books?
Correct!
Recalculate the total number of ways.
PTS: 1
DIF: Average
REF: Page 635
OBJ: 12-1.2 Solve problems involving dependent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving dependent events.
KEY: Solve Problems | Probability | Dependent Events
8. ANS: B
There is 1 choice for the first position and 5! ways for arranging the remaining 5 members.
Feedback
A
B
C
D
How many members are there in the dance group?
Correct!
How many ways are there of arranging the members on positions 2 to 6?
What type of event does the arrangement of dancers on positions 2 to 6 involve?
PTS: 1
DIF: Average
REF: Page 635
OBJ: 12-1.2 Solve problems involving dependent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving dependent events.
KEY: Solve Problems | Probability | Dependent Events
9. ANS: B
P(2 brown-haired children) = P(2 brown-haired children and 0 black-haired children)
Feedback
A
B
C
D
How many brown-haired students are there in the class?
Correct!
How many brown-haired students are to be selected?
What is the total number of ways of selecting 2 children out of 24?
PTS: 1
DIF: Average
REF: Page 645
OBJ: 12-3.1 Find the probability of events.
NAT:
NA 1 | NA 6 | NA 8 | NA 10 | NA 5
STA: CA 19.0
TOP: Find the probability of events.
KEY: Probability
10. ANS: A
P(2 black-haired children) = P(2 black-haired children and 0 brown-haired children)
Feedback
A
B
C
D
Correct!
How many brown-haired students are there in the class?
How many brown-haired students must be selected?
What is the total number of ways of selecting 2 children out of 24?
PTS: 1
DIF: Average
REF: Page 648
OBJ: 12-3.1 Find the probability of events.
NAT:
NA 1 | NA 6 | NA 8 | NA 10 | NA 5
STA: CA 19.0
TOP: Find the probability of events.
KEY: Probability
11. ANS: C
P(2 black-haired children) = P(1 brown-haired child and 1 black-haired child)
Feedback
A
B
C
D
How many brown-haired students are there in the class?
How many brown-haired students are to be selected?
Correct!
What is the total number of ways of selecting 2 children out of 24?
PTS: 1
DIF: Average
REF: Page 648
OBJ: 12-3.1 Find the probability of events.
NAT:
NA 1 | NA 6 | NA 8 | NA 10 | NA 5
STA: CA 19.0
TOP: Find the probability of events.
KEY: Probability
12. ANS: C
Use the Fundamental Counting Principle to find the number of successes C(6, 1) C(4, 2) C(3, 0).
Determine the probability P(1 science and 2 mathematics books) by using the probability formula
=
.
Feedback
A
B
C
D
You have used permutations.
Did you apply the correct Fundamental Counting Principle?
Correct!
Did you apply the correct probability formula?
PTS:
OBJ:
STA:
13. ANS:
1
DIF: Advanced
REF: Page 648
12-3.1 Find the probability of events.
NAT:
CA 19.0
TOP: Find the probability of events.
A
The probability of an event is given by the expression
NA 1 | NA 6 | NA 8 | NA 10 | NA 5
KEY: Probability
, while the odds of an event are given by the
expression s:f.
Feedback
A
B
C
D
Correct!
The odds of an event are different from the probability of that event.
This represents the probability of the failure of this event.
This represents the odds against this event.
PTS: 1
DIF: Average
REF: Page 648
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
KEY: Odds
OBJ: 12-3.2 Find the odds of events.
TOP: Find the odds of events.
14. ANS: A
The probability of an event is given by the expression
, while the odds of an event are given by the
expression s:f.
Feedback
A
B
C
D
Correct!
This represents the odds against this event.
The odds of an event are different from the probability of that event.
This represents the probability of the failure of this event.
PTS: 1
DIF: Average
REF: Page 648
OBJ: 12-3.2 Find the odds of events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Find the odds of events.
KEY: Odds
15. ANS: A
The table gives the probability of selecting different numbers of tickets bearing even numbers. Hence, the
probability corresponding to the selection of zero even-numbered tickets is
.
Feedback
A
B
C
D
Correct!
What is the number of even-numbered tickets corresponding to the shown probability in
the relative-frequency histogram?
This is the probability of selecting either one or two even-numbered tickets.
This is the probability of the failure of the given event.
PTS: 1
DIF: Basic
REF: Page 649
OBJ: 12-3.3 Create and use graphs of probability distributions. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Create and use graphs of probability distributions.
KEY: Probability | Probability Distribution Graphs
16. ANS: A
The table shows the probability of selecting different numbers of tickets bearing even numbers. The
probability of selecting three even-numbered tickets is
.
Feedback
A
B
C
D
Correct!
What is the number of even-numbered tickets corresponding to this probability in the
relative-frequency histogram?
This is the probability of selecting either one or two even-numbered tickets.
This is the probability of the failure of the given event.
PTS: 1
DIF: Basic
REF: Page 649
OBJ: 12-3.3 Create and use graphs of probability distributions. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Create and use graphs of probability distributions.
KEY: Probability | Probability Distribution Graphs
17. ANS: B
The probability P(both female kittens) = P(female kitten) · P(female kitten) as both the selections are
independent.
Feedback
A
B
C
D
Did you apply the correct formula for the probability of independent events?
Correct!
This is the probability of selecting one male kitten and one female kitten.
This is the probability of selecting two male kittens.
PTS: 1
DIF: Average
REF: Page 655
OBJ: 12-4.1 Find the probability of two independent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Find the probability of two independent events.
KEY: Probability | Independent Events
18. ANS: B
The probability P(a red, a blue, and then a green coin) = P(red coin) · P(blue coin) · P(green coin) as the three
selections are independent because each time a coin is selected, it is replaced.
Feedback
A
B
C
D
Have you used the correct formula for the probability of three independent events?
Correct!
Check the type of event.
What is the number of red coins?
PTS: 1
DIF: Average
REF: Page 655
OBJ: 12-4.1 Find the probability of two independent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Find the probability of two independent events.
KEY: Probability | Independent Events
19. ANS: A
The probability P(getting 4 on each of the 3 throws of a dice) = P(getting 4 in a single toss of a dice) ·P
(getting 4 in a single toss of a dice) · P(getting 4 in a single toss of a dice), as all the throws are independent.
Feedback
A
B
C
D
Correct!
The probability of drawing a 4 is the same in each throw.
How many times has the dice been rolled?
What is the formula for finding the probability of independent events?
PTS: 1
DIF: Average
REF: Page 655
OBJ: 12-4.1 Find the probability of two independent events.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Find the probability of two independent events.
KEY: Probability | Independent Events
20. ANS: B
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of values is the value which occurs most frequently in the given group.
Feedback
A
B
C
D
Did you find the correct value of the mode?
Correct!
The value of the mean must be calculated to the nearest tenth place.
Did you apply the correct formula for calculating the median?
PTS: 1
DIF: Average
REF: Page 667
OBJ: 12-6.1 Use measures of central tendency to represent a set of data.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Use measures of central tendency to represent a set of data.
KEY: Measures of Central Tendency | Data | Represent Data
21. ANS: B
If two events, A and B, are mutually exclusive, which means that they cannot occur at the same time, then the
probability that either A or B occurs is the sum of their probabilities.
Feedback
A
B
C
D
Recall the definition of mutually inclusive events and recalculate.
Correct!
How many cards does a standard set contain?
Can a single card have both a queen and a jack on its face?
PTS: 1
DIF: Average
REF: Page 661
OBJ: 12-5.1 Find the probability of mutually exclusive events. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Find the probability of mutually exclusive events.
KEY: Probability | Mutually Exclusive Events
22. ANS: C
If two events, A and B, are mutually exclusive, which means that the two events cannot occur at the same
time, then the probability that A or B occurs is the sum of their probabilities.
Feedback
A
B
C
D
Check the number range written on the tiles.
The number of multiples of 7 is different from the number of multiples of 8.
Correct!
The required probability is not the product of the probabilities of the two mutually
exclusive events.
PTS: 1
DIF: Advanced
REF: Page 661
OBJ: 12-5.1 Find the probability of mutually exclusive events. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Find the probability of mutually exclusive events.
KEY: Probability | Mutually Exclusive Events
23. ANS: D
If two events, A and B, are mutually exclusive, which means that the two events cannot occur at the same
time, then the probability that A or B occurs is the sum of their probabilities.
Feedback
A
B
C
D
How many multiples of 2 are there between 2 and 6?
What is the probability of getting a multiple of 5 on rolling a dice?
Have you used the correct formula for calculating the probability of these mutually
exclusive events?
Correct!
PTS: 1
DIF: Basic
REF: Page 661
OBJ: 12-5.1 Find the probability of mutually exclusive events. NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Find the probability of mutually exclusive events.
KEY: Probability | Mutually Exclusive Events
24. ANS: D
Use the formula for the margin of sampling error and round off the result to the nearest percent.
Feedback
A
B
C
D
The margin of sampling error must be calculated to the nearest percent.
Use the square root of the result of p(1 – p) / n.
The margin of error is not equal to the square root of p(1 – p) / n.
Correct!
PTS: 1
DIF: Advanced
REF: Page 684
OBJ: 12-9.2 Find margins of sampling error.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 5
TOP: Find margins of sampling error.
KEY: Margins of Sampling Error | Samples
25. ANS: D
Use the formula for the margin of sampling error and round off the result to the nearest percent.
Feedback
A
B
C
D
Use the square root of the result of p(1 – p) / n.
The margin of sampling error must be calculated to the nearest percent.
Did you calculate correctly?
Correct!
PTS: 1
DIF: Advanced
REF: Page 684
OBJ: 12-9.2 Find margins of sampling error.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 5
TOP: Find margins of sampling error.
KEY: Margins of Sampling Error | Samples
26. ANS: C
Identify the parameters of binomial distribution and calculate the given probability of the given event using
binomial expansion.
Feedback
A
B
C
D
What is the formula to calculate the probability of a binomial experiment?
This is the probability of knocking down four hurdles.
Correct!
What is the total number of hurdles to be crossed?
PTS: 1
DIF: Advanced
REF: Page 679
OBJ: 12-8.2 Find probabilities for binomial experiments.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 5
TOP: Find probabilities for binomial experiments. KEY:
Probability | Binomial Experiments
27. ANS: C
Identify the parameters of binomial distribution and calculate the probability of the given event using
binomial expansion.
Feedback
A
B
C
D
This is the probability of clearing exactly two hurdles.
Did you perform the calculations correctly?
Correct!
This is the probability of clearing more than two hurdles.
PTS:
OBJ:
TOP:
28. ANS:
1
DIF: Advanced
REF: Page 679
12-8.2 Find probabilities for binomial experiments.
Find probabilities for binomial experiments. KEY:
A
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 5
Probability | Binomial Experiments
A sample of size n is unbiased when every possible sample of size n of a population has an equal chance of
being selected.
Feedback
A
B
C
D
Correct!
People preferring Chinese food would like to go to a Chinese restaurant.
Did you select the correct type of sample?
The general preference of the surveyed people is more likely to be Thai food as they are
going to a Thai restaurant in particular.
PTS: 1
DIF: Average
REF: Page 684
OBJ: 12-9.1 Determine whether a sample is unbiased.
NAT: NA 1 | NA 6 | NA 9 | NA 10 | NA 5
TOP: Determine whether a sample is unbiased.
KEY: Samples | Bias
29. ANS: D
Find the number of standard deviations from the mean corresponding to 55 and 65 marks. Then, calculate the
percentage of data within this range of standard deviations of the mean.
Feedback
A
B
C
D
This is the percentage of students scoring more than 70 marks or less than 50 marks.
What is the percentage of data between one standard deviation below and one standard
deviation above the mean of the distribution?
Did you check the standard deviations of mean for the given marks?
Correct!
PTS: 1
DIF: Average
REF: Page 674
OBJ: 12-7.2 Solve problems involving normally distributed data.
NAT: NA 1 | NA 6 | NA 8 | NA 10 | NA 5
TOP: Solve problems involving normally distributed data.
KEY: Solve Problems | Data | Normal Distribution
30. ANS: A
Find the number of standard deviation at 45 marks. Then, using the normal distribution curve, calculate the
percentage of students scoring less than 45 marks.
Feedback
A
B
C
D
Correct!
This is the percentage of students scoring less than 50 marks or more than 70 marks.
Did you check the standard deviations above or below the mean for the value 45?
The value 45 is three standard deviations and not one standard deviation below the
mean.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: Average
REF: Page 674
12-7.2 Solve problems involving normally distributed data.
NA 1 | NA 6 | NA 8 | NA 10 | NA 5
Solve problems involving normally distributed data.
Solve Problems | Data | Normal Distribution