Download Chapter 12 - Crestwood Local Schools

Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Formulate a set of five different numbers whose median is 95 and whose
mean is 100.
Sample answer
90, 92, 95, 110, 113
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
(For help, go to Lesson 3-3.)
Find the median and mode of each data set.
1. 6, 9, 9, 5, 9
2. 73, 78, 77, 73, 79
3. 300, 100, 200, 150, 300
4. 3, 5, 7, 9, 3, 4, 6, 3, 7
Check Skills You’ll Need
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Solutions
1. 5, 6, 9, 9, 9
median = 9
mode = 9
2. 73, 73, 77, 78, 79
median = 77
mode = 73
3. 100, 150, 200, 300, 300
median = 200
mode = 300
4. 3, 3, 3, 4, 5, 6, 7, 7, 9
median = 5
mode = 3
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Quick Check
A survey asked 22 students how many hours of TV
they watched daily. The results are shown. Display the data
in a frequency table.
1 3 4 3 1 1 2 3 4 1 3
2 2 1 3 2 1 2 3 2 4 3
List the numbers of
hours in order.
Use a tally mark
for each result.
Count the tally marks and
record the frequency.
Number
Tally
Frequency
1
|||| |
6
2
|||| |
6
3
|||| ||
7
4
|||
3
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Twenty-one judges were asked how many cases they were trying
on Monday. The frequency table below shows their responses. Display the
data in a line plot. Then find the range.
“How many cases are you trying?”
Number Frequency
0
3
1
5
2
4
3
5
4
4
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
(continued)
For a line plot, follow these steps 1 , 2 , and 3 .
3 Write a title that describes the data.
Cases Tried by Judges
x
x
x
x
x
x
x
x
0
1
x
x
x
x
x
x
x
x
x
x
x
x
x
2
3
4
2 Mark an x for each
response.
1 Draw a number line with the choices below it.
The greatest value in the data set is 4 and the least value is 0. So the
range is 4 – 0, or 4.
Quick Check
12-1
Frequency Tables, Line Plots, and Histograms
PRE-ALGEBRA LESSON 12-1
Solve.
1. Maria surveyed friends to find out how
many pets each one has.
The responses are below.
Display the data in a frequency table.
0, 1, 1, 2, 3, 0, 1, 1, 3, 2, 1, 2, 1, 0, 1, 0, 0
Pets
0
1
2
3
2. Here are the numbers of books students
read in the last month: 5, 4, 0, 12, 4, 5,
4, 3, 10, 5, 12, 3, 5, 7, 3, 10, 5, 0, 6.
Display the data in a line plot.
Then find the range.
range: 12
12-1
Tally Frequency
IIII
5
IIII II
7
III
3
II
2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
If the population of the United States is approximately 250 million and the
median age is 33 yr, roughly how many people in the United States are younger
than 33 years old?
125 million
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
(For help, go to Lesson 3-3.)
Find each median.
1. 12, 10, 11, 7, 9, 8, 10, 5
2. 4.5, 3.2, 6.3, 5.2, 5, 4.8, 6, 3.9
3. 55, 53, 67, 52, 50, 49, 51, 52, 52, 52
4. 101, 100, 100, 105, 102, 101
Check Skills You’ll Need
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
Solutions
1. 5, 7, 8, 9, 10, 10, 11, 12
median =
9 + 10
= 9.5
2
2. 3.2, 3.9, 4.5, 4.8, 5, 5.2, 6, 6.3
median =
4.8 + 5
= 4.9
2
3. 49, 50, 51, 52, 52, 52, 52, 53, 55, 67
median =
52 + 52
= 52
2
4. 100, 100, 101, 101, 102, 105
median =
101 + 101
= 101
2
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
The data below represent the wingspans in
centimeters of captured birds. Make a box-and-whisker plot.
61 35 61 22 33 29 40 62 21 49 72 75 28 21 54
Step 1 Arrange the data in order from least to greatest. Find the median.
21 21 22 28 29 33 35 40 49 54 61 61 62 72 75
Step 2 Find the lower quartile and upper quartile, which are the medians of the
lower and upper halves.
21 21 22 28 29 33 35 40 49 54 61 61 62 72 75
lower quartile = 28
upper quartile = 61
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
(continued)
Step 3 Draw a number line.
Mark the least and greatest values, the median, and the quartiles.
Draw a box from the first to the third quartiles.
Mark the median with a vertical segment.
Draw whiskers from the box to the least and greatest values.
Quick Check
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
Use box-and-whisker plots to compare test scores from
two math classes.
Class A: 92, 84, 76, 68, 90, 67, 82, 71, 79, 85, 79
Class B: 78, 93, 81, 98, 69, 95, 74, 87, 81, 75, 83
Draw a number line for both sets of data. Use the range of data
points to choose a scale.
Draw the second box-and-whisker plot below the first one.
Quick Check
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
Describe the data in the box-and-whisker plot.
The lowest score is 55 and the highest is 85.
One fourth of the scores are at or below 66 and one fourth of the scores
are at or above 80.
Half of the scores are at or between 66 and 80 and thus within 10 points
of the median, 76.
Quick Check
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
The plots below compare the percents of students who
were eligible to those who participated in extracurricular activities
in one school from 1992 to 2002. What conclusions can you draw?
About 95% of the students were eligible to participate in extracurricular
activities.
Around 60% of the students did participate.
A little less than two thirds of the eligible students participated in
Quick Check
extracurricular activities.
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
Solve.
1. Use the data to make a box-and-whisker plot.
Student heights (in.) are: 60, 66, 59, 67, 68, 63, 62, 61, 69, 64, 61.
a. What is the median height?
63 in.
b. Between what heights do 50% of the students fall?
between 61 in. and 67 in.
12-2
Box-and-Whisker Plots
PRE-ALGEBRA LESSON 12-2
2. The box-and-whisker plots below compare prices for the same items
at Mary’s Discount Store and Ed’s Clothing. What conclusions can
you draw?
Prices at the discount store are more tightly grouped around the median
price of $25. Half the items cost from $18 to $45. For less expensive
items, there is not much difference in the prices at the two stores. For
more expensive items, the discount store offers lower prices.
12-2
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
Use estimation to create a circle graph. Twenty percent of the students
surveyed always prefer a salad. Thirty percent always prefer a hamburger. The
rest prefer a hamburger sometimes and a salad sometimes.
Check students’ graphs. The graphs should show 20% (72°) salad, 30%
(108°) hamburger, and 50% (180°) salad or hamburger.
12-3
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
(For help, go to Lesson 8-3.)
Find the slope of AB in each graph.
1.
2.
Check Skills You’ll Need
12-3
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
Solutions
1. 1
2
2. 1
2
12-3
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
Which title would be more appropriate for the graph
below: “Texas Overwhelms California” or “Areas of California and
Texas”? Explain.
12-3
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
(continued)
Because of the break in the vertical axis, the bar for Texas appears to be
more than six times the height of the bar for California.
Actually, the area of Texas is about 267,000 mi2, which is not even two times
the area of California, which is about 159,000 mi2.
The title “Texas Overwhelms California” could be misleading. “Areas of Texas
and California” better describes the information in the graph.
Quick Check
12-3
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
Study the graphs below. Which graph gives the impression of
a sharper increase in rainfall from March to April? Explain.
12-3
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
(continued)
In the second graph, the months are closer together and the rainfall amounts
are farther apart than in the first graph.
Thus the line appears to climb more rapidly from March to April in the
second graph.
Quick Check
12-3
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
What makes the graph misleading? Explain.
The “cake” on the right has much more than two times the area of the
cake on the left.
Quick Check
12-3
Using Graphs to Persuade
PRE-ALGEBRA LESSON 12-3
Solve.
1. Name two ways you can use graphs to give different
impressions of the same data.
Answers may vary.
Sample: Use breaks in scales;
vary the size of scale intervals.
2. What makes this graph misleading?
Explain.
Both dimensions of the “photo” on the right were changed.
This gives the impression that the difference in costs is
much greater than it really is.
12-3
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
If you roll two standard number cubes, what is the probability that the sum will
be 1? 11? Less than 4?
1
18 ; 12
0; 1
12-4
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
(For help, go to Lesson 6-4.)
A bag has 5 blue (B) chips, 4 red (R) chips, and 3 tan (T) chips.
Find each probability for choosing a chip at random from the bag.
1. P(R)
2. P(not R)
3. P(B)
4. P(R or B)
5. P(T)
6. P(B or T)
Check Skills You’ll Need
12-4
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
Solutions
1.
favorable outcomes
drawing a red chip
4
1
=
=
=
all possible outcomes
12
12
3
2.
favorable outcomes
drawing a chip that is not red
8
2
=
=
=
all possible outcomes
12
12 3
3.
favorable outcomes
drawing a blue chip
5
=
=
all possible outcomes
12
12
favorable outcomes
4. all possible outcomes =
drawing a red or blue chip
9
3
=
=
12
12
4
5.
favorable outcomes
drawing a tan chip
3
1
=
=
=
all possible outcomes
12
12
4
6.
favorable outcomes
drawing a blue or tan chip
8
2
=
=
=
all possible outcomes
12
12
3
12-4
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
The school cafeteria sells sandwiches for which you can choose
one item from each of the following categories: two breads (wheat or
white), two meats (ham or turkey), and two condiments (mayonnaise or
mustard). Draw a tree diagram to find the number of sandwich choices.
ham
wheat
turkey
ham
white
turkey
mayonnaise
mustard
mayonnaise
mustard
mayonnaise
mustard
mayonnaise
mustard
There are 8 possible sandwich choices.
12-4
Each branch of the “tree”
represents one choice—for
example, wheat-hammayonnaise.
Quick Check
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
How many two-digit numbers can be formed for which the first
digit is odd and the second digit is even?
first digit,
possible choices
5
second digit,
possible choices
•
5
numbers,
possible choices
=
25
There are 25 possible two-digit numbers in which the first digit is odd and
the second digit is even.
Quick Check
12-4
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
Quick Check
Use a tree diagram to show the sample space for guessing
right or wrong on two true-false questions. Then find the probability of
guessing correctly on both questions.
right
right
wrong
right
wrong
The tree diagram shows there are four
possible outcomes, one of which is
guessing correctly on both questions.
wrong
number of favorable outcomes
P(event) = number of possible outcomes
=
Use the probability formula.
1
4
The probability of guessing correctly on two true/false questions is 1 .
4
12-4
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
In some state lotteries, the winning number is made up of five
digits chosen at random. Suppose a player buys 5 tickets with different
numbers. What is the probability that the player has a winning number?
First find the number of possible outcomes. For each digit, there are 10
possible outcomes, 0 through 9.
1st digit
2nd digit
3rd digit
4th digit
5th digit
outcomes outcomes outcomes outcomes outcomes
•
•
•
•
10
10
10
10
10
total
outcomes
= 100,000
Then find the probability when there are five favorable outcomes.
number of favorable outcomes
5
P(winning number) = number of possible outcomes = 100,000
The probability is
5
1
, or
.
100,000
20,000
12-4
Quick Check
Counting Outcomes and Theoretical Probability
PRE-ALGEBRA LESSON 12-4
Use the following information for Questions 1 and 2. In a game, a number
cube is tossed to determine the number of spaces to move, and a coin is
tossed to determine forward or backward movement.
1. How many possible outcomes are there?
12
2. What is the theoretical probability you will move four spaces?
1
6
3. How many different three-digit whole numbers are possible using the
digits 1, 2, 3, 4, and 5?
125
12-4
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Multiply. Express the answers in lowest terms.
5
a. 3  6
5
2
1
or 2 2
b. 3  12
4
15
3
5
c. 7 
10
1
15
12-5
2
21
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
(For help, go to Lesson 5-4.)
Multiply.
1.
3 1
•
5 5
4. 5 • 4
9
8
2.
1 2
•
4 4
5. 4 • 3
7
6
3.
4
2
•
10
10
6. 9 • 8
10
9
Check Skills You’ll Need
12-5
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Solutions
3
20
2
1
12
2
2. 16 = 8
1. 25
5
4. 72 = 18
5. 42 = 7
12-5
8
2
3. 100 = 25
72
4
6. 90 = 5
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Quick Check
You roll a number cube once. Then you roll it again. What is the
probability that you get 5 on the first roll and a number less than 4 on the
second roll?
P(5) =
1
6
There is one 5 among 6 numbers on a number cube.
P(less than 4) =
3
6
There are three numbers less than 4 on a number cube.
P(5, then less than 4) = P(5) • P(less than 4)
1
3
= 6 • 6
=
3
1
, or
36
12
The probability of rolling 5 and then a number less than 4 is 1 .
12
12-5
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Bluebonnets grow wild in the southwestern United States.
Under the best conditions in the wild, each bluebonnet seed has a 20%
probability of growing. Suppose you plant bluebonnet seeds in your
garden and use a fertilizer that increases to 50% the probability that a
seed will grow. If you select two seeds at random, what is the probability
that both will grow in your garden?
P(a seed grows) = 50%, or 0.50
Write the percent as a decimal.
P(two seeds grow) = P(a seed grows) • P(a seed grows)
= 0.50 • 0.50
Substitute.
= 0.25
Multiply.
= 25%
Write 0.25 as a percent.
The probability that two seeds will grow is 25%.
12-5
Quick Check
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Three girls and two boys volunteer to represent their class at a
school assembly. The teacher selects one name and then another from a
bag containing the five students’ names. What is the probability that both
representatives will be boys?
P(boy) =
2
5
Two of five students are boys.
P(boy after boy) =
1
4
If a boy’s name is drawn, one of the four
remaining students is a boy.
P(boy, then boy) = P(boy) • P(boy after boy)
2
1
= 5 • 4
=
2
1
, or
20
10
Substitute.
Simplify.
The probability that both representatives will be boys is
12-5
1
.
10
Quick Check
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Solve.
1. You roll a number cube once. Then you roll it again. What is the
probability that you get 6 on the first roll and a number greater than 3
on the second roll?
1
12
2. Suppose there are three white marbles and three black marbles in a
bag and you want to remove two marbles. What is the probability that
you will select a white marble and then a black marble? Express your
answer as a percent.
30%
12-5
Independent and Dependent Events
PRE-ALGEBRA LESSON 12-5
Solve.
3.
Each of five girls and seven boys wants to be one of the two
announcers for a variety show. To be fair, a teacher puts the
names of the twelve students in a hat and draws two. What
is the probability that the teacher will draw the names of two
boys? Of two girls?
7
; 5
22 33
12-5
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Bianca’s family needs to choose exterior paint for their new house. The wall
colors are white, green, and beige. The trim colors are white, green, blue, and
cocoa. How many combinations of wall color and trim are possible?
12
12-6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
(For help, go to Lesson 12-4.)
Use the Counting Principle to find the number of outcomes.
1. Roll 2 number cubes.
2. Choose three different letters.
3. Select a month and a day of the week.
4. Toss a coin 4 times.
Check Skills You’ll Need
12-6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Solutions
1. first number
6 outcomes
6

2. first letter
26 choices
26

second number
6 outcomes
6
second letter
(different from 1st)
25 choices
25
= 15,600
12-6
= 36

third letter
(different from 1st & 2nd)
24 choices
24
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Solutions (continued)
3.
month
12 choices
12
4.
first toss
2 outcomes
2


day
7 choices
7
= 84
second toss
2 outcomes
2

= 16
12-6
third toss
2 outcomes
2

fourth toss
2 outcomes
2
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Find the number of permutations possible for the
letters H, O, M, E, and S.
1st letter
2nd letter
3rd letter
4th letter
5th letter
5 choices
4 choices
3 choices
2 choices
1 choice
•
•
•
•
5
4
3
2
1
= 120
There are 120 permutations of the letters H, O, M, E, and S.
Quick Check
12-6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
In how many ways can you line up 3 students chosen from 7
students for a photograph?
7 students
Choose 3.
7P3
= 7 • 6 • 5 = 210
Simplify
You can line up 3 students from 7 in 210 ways.
Quick Check
12-6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
In how many ways can you choose two states from the
table when you write reports about the areas of states?
State
Area (mi2)
Alabama
50,750
Colorado 103,729
Maine
30,865
Oregon
96,003
Texas
261,914
Make an organized list of all the combinations.
12-6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
(continued)
AL, CO AL, ME
CO, ME
AL, OR AL, TX
CO, OR CO, TX
ME, OR ME, TX
OR, TX
Use abbreviations of each
state’s name. First, list all
pairs containing Alabama.
Continue until every pair
of states is listed.
There are ten ways to choose two states from a list of five.
Quick Check
12-6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
How many different pizzas can you make if you can
choose exactly 5 toppings from 9 that are available?
9 toppings
Choose 5.
P
9 5
9C5 = P
5 5
9 • 81 • 7 • 6 2 • 51
= 5 • 4 • 3 • 2 • 1 = 126 Simplify.
1
1
1
1
You can make 126 different pizzas.
Quick Check
12-6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Tell which type of arrangement—permutations or
combinations—each problem involves. Explain.
a. How many different groups of three vegetables could you choose from
six different vegetables?
Combinations; the order of the vegetables selected does not matter.
b. In how many different orders can you play 4 DVDs?
Permutations; the order in which you play the DVDs matters.
Quick Check
12-6
Permutations and Combinations
PRE-ALGEBRA LESSON 12-6
Find the number of permutations or combinations.
1. Find the number of permutations of the last four digits in the phone
number 555–1234.
24
2. In how many ways can you arrange six out of eight books on a shelf?
20,610
3. In how many ways can you choose three different items from a menu
containing seven items?
35
Does each problem involve permutations or combinations?
4. How many different groups of four ice cream toppings can you choose
from sixteen toppings?
combinations
5. In how many different ways can five students line up?
permutations
12-6
Experimental Probability
PRE-ALGEBRA LESSON 12-7
There are 15 girls in a class of 27 students. Using lowest terms, what
fraction of the students are girls? What fraction are boys?
5
; 4
9
9
12-7
Experimental Probability
PRE-ALGEBRA LESSON 12-7
(For help, go to Lesson 6-5.)
Write each decimal or fraction as a percent.
1. 0.8
2. 0.53
3. 0.625
4. 3
5. 7
6. 5
5
12
8
Check Skills You’ll Need
12-7
Experimental Probability
PRE-ALGEBRA LESSON 12-7
Solutions
1. 0.8 = 80%
4.
3
= 0.6 = 60%
5
2. 0.53 = 53%
5.
7
1
= 0.583 = 58 %
12
3
12-7
3. 0.625 = 62.5%
6.
5
= 0.625 = 62.5%
8
Experimental Probability
PRE-ALGEBRA LESSON 12-7
A medical study tests a new medicine on 3,500 people. It
produces side effects for 1,715 people. Find the experimental
probability that the medicine will cause side effects.
number of times an event occurs
P(event) = number of times an experiment is done
1,715
= 3,500 = 0.49
The experimental probability that the medicine will cause side effects
is 0.49, or 49%.
Quick Check
12-7
Experimental Probability
PRE-ALGEBRA LESSON 12-7
Simulate the correct guessing of answers on a multiple-choice
test where each problem has four answer choices (A, B, C, and D).
Use a 4-section spinner to simulate each guess. Mark the sections as
1, 2, 3, and 4. Let “1” represent a correct choice.
Here are the results of 50 trials.
22431
32134
13431
12224
43121
42213
21243
34424
33434
32412
number of times an event occurs
10
1
P(event) = number of times an experiment is done = 50 = 5
The experimental probability of guessing correctly is
1
.
5
Quick Check
12-7
Experimental Probability
PRE-ALGEBRA LESSON 12-7
Solve.
1. Jenny made 42 out of 70 free throws. What is the experimental
probability that she will make her next free throw?
60%
2. If 152 of 722 students would choose fish for lunch, what is the
experimental probability that a student chosen at random will choose
fish?
about 21%
12-7
Random Samples and Surveys
PRE-ALGEBRA LESSON 12-8
Write and solve the proportion: The ratio of scouts to leaders is 25 to 1. If there
are 125 scouts, how many leaders are there?
25
125
; 5
=
1
5
12-8
Random Samples and Surveys
PRE-ALGEBRA LESSON 12-8
(For help, go to Lesson 6-2.)
Solve each proportion.
8
n
1. 32 = 450
2
n
3. 250 = 50,000
7
n
2. 25 = 24,000
4
n
4. 100 = 144,000
Check Skills You’ll Need
12-8
Random Samples and Surveys
PRE-ALGEBRA LESSON 12-8
Solutions
1.
8
n
=
32
450
2.
32n = 3600
25n = 168,000
32n
3600
=
32
32
168,000
25n
= 25
25
n = 112.5
3.
n
7
= 24,000
25
2
n
=
250
50,000
n = 6,720
4.
n
4
= 144,000
100
250n = 100,000
100n = 576,000
250n
100,000
=
250
250
100n
576,000
=
100
100
n = 400
n = 5,760
12-8
Random Samples and Surveys
PRE-ALGEBRA LESSON 12-8
Quick Check
You want to find out how many people in the community
use computers on a daily basis. Tell whether each survey plan
describes a good sample. Explain.
a. Interview every tenth person leaving a computer store.
This is not a good sample. People leaving a computer store are more
likely to own computers.
b. Interview people at random at the shopping center.
This is a good sample. It is selected at random from the population you
want to study.
c. Interview every tenth student who arrives at school on a school bus.
This is not a good sample. This sample will be composed primarily of
students, but the population you are investigating is the whole community.
12-8
Random Samples and Surveys
PRE-ALGEBRA LESSON 12-8
From 20,000 calculators produced, a manufacturer takes a
random sample of 300 calculators. The sample has 2 defective calculators.
Estimate the total number of defective calculators.
defective sample calculators
defective calculators
=
sample calculators
calculators
2
n
=
300
20,000
2(20,000) = 300n
2(20,000) 300n
= 300
300
133
Write a proportion.
Substitute.
Write cross products.
Divide each side by 300.
Simplify.
n
Estimate: About 133 calculators are defective.
12-8
Quick Check
Random Samples and Surveys
PRE-ALGEBRA LESSON 12-8
Solve.
1. To find out the type of music the general population prefers, you
survey people at random at a local art museum. Does the survey plan
describe a good sample?
Not a good sample; it includes only people who visit the art museum.
2. Of 80 sweaters, 6 have flaws. Estimate how many of 38,000 sweaters
have flaws.
2,850 sweaters
12-8
Problem Solving Strategy: Simulate the Problem
PRE-ALGEBRA LESSON 12-9
In a certain part of a state, only the letters J, K, L, M, and N can be used to
form a 2-letter beginning for a license plate. How many different 2-letter
beginnings are possible?
25 beginnings; 20 using two different letters and 5 using the same letter twice
12-9
Problem Solving Strategy: Simulate the Problem
PRE-ALGEBRA LESSON 12-9
(For help, go to Lesson 12-1.)
Create a frequency table showing the number of times each letter
of the alphabet appears in the sentence below.
A simulation is a model of a real experience.
Check Skills You’ll Need
12-9
Problem Solving Strategy: Simulate the Problem
PRE-ALGEBRA LESSON 12-9
Solutions
12-9
Problem Solving Strategy: Simulate the Problem
PRE-ALGEBRA LESSON 12-9
A softball player has an average of getting a base hit 2
times in every 7 times at bat. What is an experimental probability
that she will get a base hit the next time she is at bat?
You can use a spinner to simulate the problem.
Construct a spinner with seven congruent
sections. Make five of the sections blue and
two of them red. The blue sections represent
not getting a base hit and the red sections
represent getting a base hit. Each spin
represents one time at bat.
12-9
Problem Solving Strategy: Simulate the Problem
PRE-ALGEBRA LESSON 12-9
(continued)
Use the results given in the table below. “B” stands for blue and “R” stands
for red.
B
B
R
B
B
B
R
B
B
B
B
R
B
B
B
B
B
B
R
B
B
B
B
B
R
B
B
B
R
B
B
B
R
B
B
R
B
B
B
B
R
R
B
B
B
R
B
B
B
B
R
B
B
B
B
B
B
B
R
R
B
B
B
B
R
B
B
R
B
B
B
B
B
B
B
B
B
R
B
B
R
B
R
B
B
B
B
B
B
B
B
R
B
B
B
R
B
B
B
R
12-9
Problem Solving Strategy: Simulate the Problem
PRE-ALGEBRA LESSON 12-9
(continued)
Make a frequency table.
Makes a Base Hit
|||| |||| |||| |||| ||
Doesn’t Make a Base Hit
|||| |||| |||| |||| |||| |||| |||| ||||
|||| |||| |||| |||| |||| |||| |||| |||
An experimental probability that she gets a base hit the next time she
is at bat is 0.22, or 22%.
Quick Check
12-9
Problem Solving Strategy: Simulate the Problem
PRE-ALGEBRA LESSON 12-9
1. You and a friend play a game in which you each toss a coin. You score a
point for each heads and your friend scores a point for each tails. The
first person to score ten points wins. The score is 8 to 6 in your favor.
Describe a simulation that completes the game and use it to find an
experimental probability that your friend will win.
Check students’ work.
12-9