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12-1
Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and HistogramsPRE-ALGEBRA LESSON 12-1PRE-ALGEBRA LESSON 12-1
Formulate a set of five different numbers whose median is 95 and whose mean is 100.
90, 92, 95, 110, 113
Sample answer
Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and HistogramsPRE-ALGEBRA LESSON 12-1PRE-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
PRE-ALGEBRA LESSON 12-1PRE-ALGEBRA LESSON 12-1
Solutions
1. 5, 6, 9, 9, 9 2. 73, 73, 77, 78, 79median = 9 median = 77mode = 9 mode = 73
3. 100, 150, 200, 300, 300 4. 3, 3, 3, 4, 5, 6, 7, 7, 9median = 200 median = 5mode = 300 mode = 3
Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and Histograms
12-1
A survey asked 22 students how many hours of TV
they watched daily. The results are shown. Display the data
in a frequency table.
PRE-ALGEBRA LESSON 12-1PRE-ALGEBRA LESSON 12-1
1 3 4 3 1 1 2 3 4 1 32 2 1 3 2 1 2 3 2 4 3
Number Tally Frequency
List the numbers of hours in order.
1
2
3
4
Count the tally marks andrecord the frequency.
3
7
6
6
Use a tally mark for each result.
|||
|||| |
|||| |
|||| ||
Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and Histograms
Quick Check
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.
PRE-ALGEBRA LESSON 12-1PRE-ALGEBRA LESSON 12-1
“How many cases are you trying?”
Number Frequency 0 3 1 5 2 4 3 5 4 4
Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and Histograms
12-1
(continued)
PRE-ALGEBRA LESSON 12-1PRE-ALGEBRA LESSON 12-1
The greatest value in the data set is 4 and the least value is 0. So the range is 4 – 0, or 4.
For a line plot, follow these steps 1 , 2 , and 3 .
3 Write a title that describes the data.Cases Tried by Judges
2 Mark an x for each response.
x xx x x x
x x x x xx x x x xx x x x x
1 Draw a number line with the choices below it.
0 1 2 3 4
Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and Histograms
Quick Check
12-1
PRE-ALGEBRA LESSON 12-1PRE-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
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.
Pets Tally Frequency0 IIII 51 IIII II 72 III 33 II 2
range: 12
Frequency Tables, Line Plots, and HistogramsFrequency Tables, Line Plots, and Histograms
12-1
Box-and-Whisker PlotsBox-and-Whisker PlotsPRE-ALGEBRA LESSON 12-2PRE-ALGEBRA LESSON 12-2
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
Box-and-Whisker PlotsBox-and-Whisker PlotsPRE-ALGEBRA LESSON 12-2PRE-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 PlotsBox-and-Whisker PlotsPRE-ALGEBRA LESSON 12-2PRE-ALGEBRA LESSON 12-2
Solutions
1. 5, 7, 8, 9, 10, 10, 11, 12
median = = 9.5
2. 3.2, 3.9, 4.5, 4.8, 5, 5.2, 6, 6.3
median = = 4.9
3. 49, 50, 51, 52, 52, 52, 52, 53, 55, 67
median = = 52
4. 100, 100, 101, 101, 102, 105
median = = 101
9 + 102
4.8 + 52
52 + 522
101 + 1012
12-2
Box-and-Whisker PlotsBox-and-Whisker Plots
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
PRE-ALGEBRA LESSON 12-2PRE-ALGEBRA LESSON 12-2
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 75lower quartile = 28upper quartile = 61
12-2
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.
Box-and-Whisker PlotsBox-and-Whisker PlotsPRE-ALGEBRA LESSON 12-2PRE-ALGEBRA LESSON 12-2
(continued)
Quick Check
12-2
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.
Box-and-Whisker PlotsBox-and-Whisker Plots
Use box-and-whisker plots to compare test scores from
two math classes.
PRE-ALGEBRA LESSON 12-2PRE-ALGEBRA LESSON 12-2
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
Quick Check
12-2
Box-and-Whisker PlotsBox-and-Whisker Plots
Describe the data in the box-and-whisker plot.
PRE-ALGEBRA LESSON 12-2PRE-ALGEBRA LESSON 12-2
The lowest score is 55 and the highest is 85.
Half of the scores are at or between 66 and 80 and thus within 10 points of the median, 76.
One fourth of the scores are at or below 66 and one fourth of the scores are at or above 80.
Quick Check
12-2
Box-and-Whisker PlotsBox-and-Whisker Plots
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?
PRE-ALGEBRA LESSON 12-2PRE-ALGEBRA LESSON 12-2
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 extracurricular activities. Quick Check
12-2
Box-and-Whisker PlotsBox-and-Whisker PlotsPRE-ALGEBRA LESSON 12-2PRE-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?
b. Between what heights do 50% of the students fall?
63 in.
between 61 in. and 67 in.
12-2
Box-and-Whisker PlotsBox-and-Whisker PlotsPRE-ALGEBRA LESSON 12-2PRE-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 PersuadeUsing Graphs to PersuadePRE-ALGEBRA LESSON 12-3PRE-ALGEBRA LESSON 12-3
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.
Using Graphs to PersuadeUsing Graphs to PersuadePRE-ALGEBRA LESSON 12-3PRE-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 PersuadeUsing Graphs to PersuadePRE-ALGEBRA LESSON 12-3PRE-ALGEBRA LESSON 12-3
Solutions
1. 2.12
12
12-3
Using Graphs to PersuadeUsing Graphs to Persuade
Which title would be more appropriate for the graph
below: “Texas Overwhelms California” or “Areas of California and
Texas”? Explain.
PRE-ALGEBRA LESSON 12-3PRE-ALGEBRA LESSON 12-3
12-3
Using Graphs to PersuadeUsing Graphs to Persuade
(continued)
PRE-ALGEBRA LESSON 12-3PRE-ALGEBRA LESSON 12-3
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 PersuadeUsing Graphs to Persuade
Study the graphs below. Which graph gives the impression of
a sharper increase in rainfall from March to April? Explain.
PRE-ALGEBRA LESSON 12-3PRE-ALGEBRA LESSON 12-3
12-3
Using Graphs to PersuadeUsing Graphs to Persuade
(continued)
PRE-ALGEBRA LESSON 12-3PRE-ALGEBRA LESSON 12-3
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 PersuadeUsing Graphs to Persuade
What makes the graph misleading? Explain.
PRE-ALGEBRA LESSON 12-3PRE-ALGEBRA LESSON 12-3
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 PersuadeUsing Graphs to PersuadePRE-ALGEBRA LESSON 12-3PRE-ALGEBRA LESSON 12-3
Solve.
1. Name two ways you can use graphs to give different impressions of the same data.
2. What makes this graph misleading? Explain.
Answers may vary. Sample: Use breaks in scales; vary the size of scale intervals.
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 ProbabilityCounting Outcomes and Theoretical ProbabilityPRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
12-4
If you roll two standard number cubes, what is the probability that the sum will be 1? 11? Less than 4?
118
0; 112;
Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical ProbabilityPRE-ALGEBRA LESSON 12-4PRE-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 ProbabilityCounting Outcomes and Theoretical ProbabilityPRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
Solutions
1.
2.
3.
4.
5.
6.
favorable outcomesall possible outcomes =
drawing a blue chip12 =
512
13
412
favorable outcomesall possible outcomes =
drawing a red chip12 = =
favorable outcomesall possible outcomes =
drawing a chip that is not red12 =
812 =
23
favorable outcomesall possible outcomes =
drawing a red or blue chip12 =
912 =
34
favorable outcomesall possible outcomes =
drawing a tan chip12 =
312 =
14
favorable outcomesall possible outcomes =
drawing a blue or tan chip12 =
812 =
23
12-4
Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical Probability
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.
PRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
There are 8 possible sandwich choices.
mayonnaise
Each branch of the “tree” represents one choice—for example, wheat-ham-mayonnaise.
wheat
white
ham
turkey
ham
turkey
mayonnaisemustardmayonnaisemustardmayonnaisemustard
mustard
Quick Check
12-4
Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical Probability
How many two-digit numbers can be formed for which the first
digit is odd and the second digit is even?
PRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
There are 25 possible two-digit numbers in which the first digit is odd and the second digit is even.
5 • 5 = 25
first digit,possible choices
second digit,possible choices
numbers,possible choices
Quick Check
12-4
Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical Probability
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.
PRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
The tree diagram shows there are four possible outcomes, one of which is guessing correctly on both questions.
P(event) = Use the probability formula.number of favorable outcomesnumber of possible outcomes
The probability of guessing correctly on two true/false questions is .14
rightright
wrong
right
wrongwrong
=14
Quick Check
12-4
Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical Probability
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?
PRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
First find the number of possible outcomes. For each digit, there are 10 possible outcomes, 0 through 9.
1st digitoutcomes
10
2nd digitoutcomes
10
3rd digitoutcomes
10
5th digitoutcomes
10
4th digitoutcomes
10
totaloutcomes= 100,000• • • •
Then find the probability when there are five favorable outcomes.
P(winning number) = =number of favorable outcomesnumber of possible outcomes
5100,000
5100,000
The probability is , or .120,000 Quick Check
12-4
Counting Outcomes and Theoretical ProbabilityCounting Outcomes and Theoretical ProbabilityPRE-ALGEBRA LESSON 12-4PRE-ALGEBRA LESSON 12-4
Use the following information for Questions 1 and 2. In a game, a numbercube is tossed to determine the number of spaces to move, and a coin istossed to determine forward or backward movement.
1. How many possible outcomes are there?
2. What is the theoretical probability you will move four spaces?
3. How many different three-digit whole numbers are possible using the digits 1, 2, 3, 4, and 5?
125
12
16
12-4
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
12-5
3 4
Multiply. Express the answers in lowest terms.
3 b. 5 6
a. 12 15
c. 710
2 21
5 2 or 2 1
2 3 5
115
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
(For help, go to Lesson 5-4.)
Multiply.
1. • 2. • 3. •
4. • 5. • 6. •
35
15
14
24
47
36
59
48
410
210
910
89
Check Skills You’ll Need
12-5
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
Solutions
1. 2. 3.
4. 5. 6. 518
325
2072 =
18
216 =
27
1242 =
45
7290 =
8100
225=
12-5
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
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?
The probability of rolling 5 and then a number less than 4 is .112
P(5, then less than 4) = P(5) • P(less than 4)
= •16
36
336
112
= , or
P(5) =16 There is one 5 among 6 numbers on a number cube.
P(less than 4) =36 There are three numbers less than 4 on a number cube.
Quick Check
12-5
Independent and Dependent EventsIndependent and Dependent Events
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?
PRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
P(two seeds grow) = P(a seed grows) • P(a seed grows)
The probability that two seeds will grow is 25%.
P(a seed grows) = 50%, or 0.50 Write the percent as a decimal.
= 0.50 • 0.50 Substitute.
= 0.25 Multiply.
= 25% Write 0.25 as a percent.
Quick Check
12-5
Independent and Dependent EventsIndependent and Dependent Events
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?
PRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
P(boy, then boy) = P(boy) • P(boy after boy)
The probability that both representatives will be boys is .110
220
110
= , or Simplify.
= •25
14
Substitute.
P(boy after boy) =14
If a boy’s name is drawn, one of the four remaining students is a boy.
P(boy) =25 Two of five students are boys.
Quick Check
12-5
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-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?
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%
112
12-5
Independent and Dependent EventsIndependent and Dependent EventsPRE-ALGEBRA LESSON 12-5PRE-ALGEBRA LESSON 12-5
Solve.
722
533
;
12-5
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?
Permutations and CombinationsPermutations and CombinationsPRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
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
Permutations and CombinationsPermutations and CombinationsPRE-ALGEBRA LESSON 12-6PRE-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 CombinationsPermutations and CombinationsPRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
Solutions
1. first number second number6 outcomes 6 outcomes
6 6 = 36
2. first letter second letter third letter(different from 1st) (different from 1st & 2nd)
26 choices 25 choices 24 choices
26 25 24
= 15,600
12-6
Permutations and CombinationsPermutations and CombinationsPRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
Solutions (continued)
3. month day12 choices 7 choices
12 7 = 84
4. first toss second toss third toss fourth toss2 outcomes 2 outcomes 2 outcomes 2 outcomes
2 2 2 2
= 16
12-6
Permutations and CombinationsPermutations and Combinations
Find the number of permutations possible for the
letters H, O, M, E, and S.
PRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
1st letter5 choices
5
2nd letter4 choices
4
3rd letter3 choices
3
5th letter1 choice
1
4th letter2 choices
2 = 120• • • •
There are 120 permutations of the letters H, O, M, E, and S.
Quick Check
12-6
Permutations and CombinationsPermutations and Combinations
In how many ways can you line up 3 students chosen from 7
students for a photograph?
PRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
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 CombinationsPermutations and Combinations
In how many ways can you choose two states from the
table when you write reports about the areas of states?
PRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
State Area (mi2)Alabama ColoradoMaine Oregon Texas
50,750103,72930,86596,003
261,914
Make an organized list of all the combinations.
12-6
Permutations and CombinationsPermutations and Combinations
(continued)
PRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
AL, CO AL, ME AL, OR AL, TX Use abbreviations of each CO, ME CO, OR CO, TX state’s name. First, list all
ME, OR ME, TX pairs containing Alabama. OR, TX 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 CombinationsPermutations and Combinations
How many different pizzas can you make if you can
choose exactly 5 toppings from 9 that are available?
PRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
9 toppings Choose 5.
9C5= 9P5
5P5
You can make 126 different pizzas.
= = 126 Simplify.9 • 81 • 7 • 62 • 51
51 • 41 • 31 • 21 • 1
Quick Check
12-6
Permutations and CombinationsPermutations and Combinations
Tell which type of arrangement—permutations or
combinations—each problem involves. Explain.
PRE-ALGEBRA LESSON 12-6PRE-ALGEBRA LESSON 12-6
a. How many different groups of three vegetables could you choose from six different vegetables?
b. In how many different orders can you play 4 DVDs?
Combinations; the order of the vegetables selected does not matter.
Permutations; the order in which you play the DVDs matters.
Quick Check
12-6
Permutations and CombinationsPermutations and CombinationsPRE-ALGEBRA LESSON 12-6PRE-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.
2. In how many ways can you arrange six out of eight books on a shelf?
3. In how many ways can you choose three different items from a menu containing seven items?
Does each problem involve permutations or combinations?
4. How many different groups of four ice cream toppings can you choose from sixteen toppings?
5. In how many different ways can five students line up?
35
24
20,610
combinations
permutations
12-6
Experimental ProbabilityExperimental ProbabilityPRE-ALGEBRA LESSON 12-7PRE-ALGEBRA LESSON 12-7
12-7
There are 15 girls in a class of 27 students. Using lowest terms, whatfraction of the students are girls? What fraction are boys?
59
49
;
Experimental ProbabilityExperimental ProbabilityPRE-ALGEBRA LESSON 12-7PRE-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. 5. 6.35
58
712
Check Skills You’ll Need
12-7
Experimental ProbabilityExperimental ProbabilityPRE-ALGEBRA LESSON 12-7PRE-ALGEBRA LESSON 12-7
Solutions
1. 0.8 = 80% 2. 0.53 = 53% 3. 0.625 = 62.5%
4. = 0.6 = 60% 5. = 0.583 = 58 % 6. = 0.625 = 62.5%35
58
712
13
12-7
Experimental ProbabilityExperimental Probability
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.
PRE-ALGEBRA LESSON 12-7PRE-ALGEBRA LESSON 12-7
The experimental probability that the medicine will cause side effects is 0.49, or 49%.
P(event) = number of times an event occurs
number of times an experiment is done
= = 0.491,7153,500
Quick Check
12-7
Experimental ProbabilityExperimental Probability
Simulate the correct guessing of answers on a multiple-choice test
where each problem has four answer choices (A, B, C, and D).
PRE-ALGEBRA LESSON 12-7PRE-ALGEBRA LESSON 12-7
Use a 4-section spinner to simulate each guess. Mark the sections as 1, 2, 3, and 4. Let “1” represent a correct choice.
P(event) = = = number of times an event occurs
number of times an experiment is done15
1050
Here are the results of 50 trials.
22431 13431 43121 21243 3343432134 12224 42213 34424 32412
The experimental probability of guessing correctly is .15
Quick Check
12-7
Experimental ProbabilityExperimental ProbabilityPRE-ALGEBRA LESSON 12-7PRE-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?
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%
60%
12-7
Random Samples and SurveysRandom Samples and SurveysPRE-ALGEBRA LESSON 12-8PRE-ALGEBRA LESSON 12-8
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?
251
1255
= ; 5
Random Samples and SurveysRandom Samples and SurveysPRE-ALGEBRA LESSON 12-8PRE-ALGEBRA LESSON 12-8
(For help, go to Lesson 6-2.)
Solve each proportion.
1. = 2. =
3. = 4. =
n450
832
n24,000
725
4100
n144,000
2250
n50,000
Check Skills You’ll Need
12-8
Random Samples and SurveysRandom Samples and SurveysPRE-ALGEBRA LESSON 12-8PRE-ALGEBRA LESSON 12-8
Solutions
1. = 2. =
32n = 3600 25n = 168,000
= =
n = 112.5 n = 6,720
3. = 4. =
250n = 100,000 100n = 576,000
= =
n = 400 n = 5,760
n450
832
n24,000
725
4100
n144,000
2250
n50,000
32n32
360032
25n25
168,00025
250n250
100,000250
100n100
576,000100
12-8
Random Samples and SurveysRandom Samples and Surveys
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.
PRE-ALGEBRA LESSON 12-8PRE-ALGEBRA LESSON 12-8
a. Interview every tenth person leaving a computer store.
b. Interview people at random at the shopping center.
c. Interview every tenth student who arrives at school on a school bus.
This is not a good sample. People leaving a computer store are more likely to own computers.
This is a good sample. It is selected at random from the population you want to study.
This is not a good sample. This sample will be composed primarily of students, but the population you are investigating is the whole community.
Quick Check
12-8
Random Samples and SurveysRandom Samples and Surveys
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.
PRE-ALGEBRA LESSON 12-8PRE-ALGEBRA LESSON 12-8
Estimate: About 133 calculators are defective.
defective sample calculatorssample calculators
defective calculatorscalculators= Write a proportion.
2300
n20,000= Substitute.
2(20,000) = 300n Write cross products.
2(20,000)300
300n300= Divide each side by 300.
133 n Simplify.
Quick Check
12-8
Random Samples and SurveysRandom Samples and SurveysPRE-ALGEBRA LESSON 12-8PRE-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?
2. Of 80 sweaters, 6 have flaws. Estimate how many of 38,000 sweaters have flaws.
2,850 sweaters
Not a good sample; it includes only people who visit the art museum.
12-8
Problem Solving Strategy: Simulate the ProblemProblem Solving Strategy: Simulate the ProblemPRE-ALGEBRA LESSON 12-9PRE-ALGEBRA LESSON 12-9
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
Problem Solving Strategy: Simulate the ProblemProblem Solving Strategy: Simulate the ProblemPRE-ALGEBRA LESSON 12-9PRE-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
PRE-ALGEBRA LESSON 12-9PRE-ALGEBRA LESSON 12-9
Solutions
Problem Solving Strategy: Simulate the ProblemProblem Solving Strategy: Simulate the Problem
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?
PRE-ALGEBRA LESSON 12-9PRE-ALGEBRA LESSON 12-9
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.
Problem Solving Strategy: Simulate the ProblemProblem Solving Strategy: Simulate the Problem
12-9
(continued)
PRE-ALGEBRA LESSON 12-9PRE-ALGEBRA LESSON 12-9
Use the results given in the table below. “B” stands for blue and “R” stands for red.
B B B B R R B B R BB R B B R B B B B RR B B R B B B B R BB B B B B B B B B BB B R B B B R B B BB B B R R B B B B RR B B B B B B B B BB B B B B B R R B BB R R B B R B B B BB B B B B R B B B R
Problem Solving Strategy: Simulate the ProblemProblem Solving Strategy: Simulate the Problem
12-9
(continued)
PRE-ALGEBRA LESSON 12-9PRE-ALGEBRA LESSON 12-9
Make a frequency table.
An experimental probability that she gets a base hit the next time she is at bat is 0.22, or 22%.
Makes a Base Hit Doesn’t Make a Base Hit |||| |||| |||| |||| || |||| |||| |||| |||| |||| |||| |||| ||||
|||| |||| |||| |||| |||| |||| |||| |||
Problem Solving Strategy: Simulate the ProblemProblem Solving Strategy: Simulate the Problem
Quick Check
12-9
PRE-ALGEBRA LESSON 12-9PRE-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.
Problem Solving Strategy: Simulate the ProblemProblem Solving Strategy: Simulate the Problem
12-9