12-6

12-6 Making Predictions

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm Up

1. Zachary rolled a fair number cube twice. Find the probability of the number cube showing an odd number both times.

2. Larissa rolled a fair number cube twice. Find the probability of the number cube showing the same number both times.

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12-6 Making Predictions

1

4__

1

36___

Problem of the Day

The average of three numbers is 45. If the average of the first two numbers is 47, what is the third number?

41

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12-6 Making Predictions

Learn to use probability to predict events.

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12-6 Making Predictions

Vocabulary

prediction

population

sample

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12-6 Making Predictions

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A prediction is a guess about something in the future. One way to make a prediction is to collect information by conducting a survey. The population is the whole group being surveyed. To save time and money; researchers often make predictions based on a sample, which is part of the group being surveyed. Another way to make a prediction is to use probability.

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12-6 Making Predictions

Additional Example 1: Using Sample Surveys to Make Prediction

A store claims that 78% of shoppers end up buying something. Out of 1,000 shoppers, how many would you predict will buy something?

You can write a proportion. Remember that percent means “per hundred.”

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12-6 Making Predictions

Additional Example 1 Continued

100x 100 ____ 78,000

100 ______

=Divide both sides by 100 to undo the multiplication.

x = 780

You can predict that about 780 out of 1,000 customers will buy something.

Think: 78 out of 100 is how many out of 1,000.

100 • x = 78 • 1,000

100x = 78,000

The cross products are equal.

x is multiplied by 100.

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12-6 Making Predictions

78100___ x

1,000=

Check It Out: Example 1

A store claims 62% of shoppers end up buying something. Out of 1,000 shoppers, how many would you predict will buy something?

You can write a proportion. Remember that percent means “per hundred.”

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12-6 Making Predictions

Check It Out: Example 1 Continued

100x 100 ____ 62,000

100 ______

=Divide both sides by 100 to undo the multiplication.

x = 620

You can predict that about 620 out of 1,000 customers will buy something.

Think: 62 out of 100 is how many out of 1,000.

100 • x = 62 • 1,000

100x = 62,000

The cross products are equal.

x is multiplied by 100.

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12-6 Making Predictions

62100___ x

1,000=

Additional Example 2: Using Theoretical Probability to Make Predictions

If you roll a number cube 30 times, how many times do you expect to roll a number greater than 2?

2 3 __ x

30 ___=

Think: 2 out of 3 is how many out of 30.

3 • x = 2 • 30

3x = 60

The cross products are equal.

x is multiplied by 3.

P(greater than 2) = = 4

6__ 2

3__

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12-6 Making Predictions

Additional Example 2 Continued

Divide both sides by 3 to undo the multiplication.

x = 20

You can expect to roll a number greater than 2 about 20 times.

3x 3 __ 60

3 __

=

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12-6 Making Predictions

Check It Out: Example 2

If you roll a number cube 30 times, how many times do you expect to roll a number greater than 3?

1 2 __ x

30 ___=

Think: 1 out of 2 is how many out of 30.

2 • x = 1 • 30

2x = 30

The cross products are equal.

x is multiplied by 2.

P(greater than 3) = = 3

6__ 1

2__

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12-6 Making Predictions

Check It Out: Example 2 Continued

Divide both sides by 2 to undo the multiplication.

x = 15

You can expect to roll a number greater than 3 about 15 times.

2x 2 __ 30

2 __

=

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12-6 Making Predictions

Additional Example 3: Problem Solving Application

Suppose the managers of a second stadium, like the one in the student book, also sell yearly parking passes.

The managers of the second stadium estimate that the probability of a person with a pass attending any one event is 50%. The parking lot has 400 spaces. If the managers want the lot to be full at every event, how many passes should they sell?

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12-6 Making Predictions

11 Understand the Problem

The answer will be the number of parking passes they should sell.

List the important information:

• P(person with pass attends event): = 50%

• There are 400 parking spaces

The managers want to fill all 400 spaces. But on average, only 50% of parking pass holders will attend. So 50% of pass holders must equal 400. You can write an equation to find this number.

22 Make a Plan

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12-6 Making Predictions

Solve33

50100___ 400

x____=

Think: 50 out of 100 is 400 out of how many?

100 • 400 = 50 • x

40,000 = 50x

The cross products are equal.

x is multiplied by 50.

40,000 50 ______ 50x

50 ___ =

Divide both sides by 50 to undo the multiplication.

800 = x

The managers should sell 800 parking passes.

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12-6 Making Predictions

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If the managers sold only 400 passes, the parking lot would not usually be full because only about 50% of the people with passes will attend any one event. The managers should sell more than 400 passes, so 800 is a reasonable answer.

Look Back44

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12-6 Making Predictions

Check It Out: Example 3

The concert hall managers sell annual memberships. If you have an annual membership, you can attend any event during that year.

The managers estimate that the probability of a person with a membership attending any one event is 60%. The concert hall has 600 seats. If the managers want the seats to be full at every event, how many memberships should they sell?

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12-6 Making Predictions

11 Understand the Problem

The answer will be the number of membership they should sell.

List the important information:

• P(person with membership attends event): = 60%

• There are 600 seats

The managers want to fill all 600 seats. But on average, only 60% of membership holders will attend. So 60% of membership holders must equal 600. You can write an equation to find this number.

22 Make a Plan

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12-6 Making Predictions

Solve33

60100___ 600

x____=

Think: 60 out of 100 is 600 out of how many?

100 • 600 = 60 • x

60,000 = 60x

The cross products are equal.

x is multiplied by 60.

60,000 60 ______ 60x

60 ___ =

Divide both sides by 60 to undo the multiplication.

1,000 = x

The managers should sell 1,000 annual memberships.

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12-6 Making Predictions

Insert Lesson Title Here

If the managers sold only 600 annual memberships, the seats would not usually be full because only about 60% of the people with memberships will attend any one event. The managers should sell more than 600 passes, so 1,000 is a reasonable answer.

Look Back44

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12-6 Making Predictions

Lesson Quiz: Part I

1. The owner of a local pizzeria estimates that 72% of his customers order pepperoni on their on their pizza. Out of 250 orders taken in one day, how many would you predict to have pepperoni? 180

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12-6 Making Predictions

Lesson Quiz: Part II

2. A bag contains 9 red chips, 4 blue chips, and 7 yellow chips. You pick a chip from the bag, record its color, and put the chip back in the bag. If you do this 100 times, how many times do you expect to remove a yellow chip from the bag?

3. A quality-control inspector has determined that 3% of the items he checks are defective. If the company he works for produces 3,000 items per day, how many does the inspector predict will be defective?

35

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90

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12-6 Making Predictions