##### Document Text Contents

Page 1

What You’ll Learn

• Understand how probability is used in everyday situations.

• Identify and solve problems related to data collection.

• Use either a population or a sample to answer a question.

• Develop and carry out a plan to collect, display, and analyze data.

343

9

UNIT

Probability and Statistics

Why It’s Important

Probability is used by

• weather forecasters to more accurately predict the weather

• insurance companies to help determine insurance premiums

Key Words

experimental probability

theoretical probability

subjective judgment

assumptions

fair

biased question

census

population

sample

valid conclusions

simple random sampling

systematic sampling

cluster sampling

self-selected sampling

convenience sampling

stratified random sampling

MMS9_Prep book_Unit9.1.qxp 7/8/09 4:42 PM Page 343

Page 2

12% � � 3

25

12

100

Check

1. Write each fraction as a percent.

a) � ________ b) � c) �

� �

� ________ �

2. Write each fraction as a decimal.

a) � ________ b) � ____________ c) � ____________

� ________ � ________

3. Write each percent as a fraction in simplest form.

a) 27% � b) 25% � c) 70% �

� �

� �

100 � 25

100

100

100

3

8

13

50

17

100

100

3

20

2 �

5 � 20

2

5

35

100

9.1 Skill Builder

Relating Fractions, Decimals, and Percents

This hundredths chart represents one whole, 1, or 100%.

The shaded part of this grid can be described in 3 ways.

As a fraction:

As a decimal: 0.16

As a percent: 16%

16

100

Write a fraction as a percent: Write a percent as a fraction:

� 25

� � 75%

� 25

Write a fraction as a decimal:

75

100

3

4

� 1 � 2 � 0.51

2

We can also read as 16 out of 100.16

100

We can think of a

fraction as division.

� 4

� 4

344

MMS9_Prep book_Unit9.1.qxp 7/8/09 4:42 PM Page 344

Page 18

360

The school council wants to know if students would like to have a dance to

celebrate the end of the school year. The council surveys 2 girls from each

grade to find out.

Was a sample or a census used to collect the data?

Do you think the conclusions would be valid? Explain.

Solution

Not all students in the school were surveyed. So, the data were collected from a sample.

All students surveyed were girls. And, 2 students from each grade is probably not enough to

represent the population. So, the conclusions are probably not valid. More students should be

surveyed, with a proportional number of boys and girls included.

Identifying and Critiquing the Use of SamplesExample 3

Check

In each case, was a sample or a census used to collect the data?

Wherever a sample was used, do you think the conclusions would be valid?

Explain.

1. To find out what percent of the population of British Columbia has access to

the Internet, all residents of Victoria were surveyed.

What is the population? ___________________________________

Were all residents surveyed? _______

Was a sample or census used? ____________

Do you think the results of the survey would represent the residents of a small

northern mining community? _______

Do you think the conclusions would be valid? _______

2. To ensure safe and secure air travel from Edmonton International Airport,

anyone boarding a plane at the airport goes through a security check.

What is the population? ________________________________________________

_________________________________________________________________________

Were all people boarding planes checked? _______

Was a sample or a census used? ___________

MMS9_Prep book_Unit9.3.qxd 7/8/09 4:43 PM Page 360

Page 19

361

3. To find out the favourite flavour of bubble tea, every fifth customer of the

bubble tea café is surveyed.

What is the population? ____________________________

Were all customers surveyed? _______

Was a sample or a census used? ____________

Do you think the conclusions would be valid? _______ Why?

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Practice

1. Identify the population of each survey.

a) The manager of an apartment building wants to find out which apartments

in the building need new carpet.

__________________________________________________________________________________

b) The manager of a video game store in Grande Prairie wants to find out

how many video games are owned by the average teenager in town.

__________________________________________________________________________________

c) A company that manufactures programmable thermostats wants to test its

thermostats for defects.

__________________________________________________________________________________

2. In each case, describe why a sample was used instead of a census.

a) A car company in Canada wants to find out whether people plan to buy or

lease their next vehicle.

__________________________________________________________________________________

__________________________________________________________________________________

b) A clothing manufacturer wants to make sure the guarantee that its clothing

will not shrink when washed is upheld.

__________________________________________________________________________________

__________________________________________________________________________________

MMS9_Prep book_Unit9.3.qxd 7/8/09 4:43 PM Page 361

Page 35

377

9.3

4. Explain why this survey might be problematic.

a) A tourist attraction employs 500 students for the summer. They want to find

out how much money students save from each pay cheque. They plan to

survey each student as he or she is given the next pay cheque.

Is there a problem with time or cost? ______

Is there a problem with privacy? ______

Is there a problem with cultural sensitivity? ______

Explain. _______________________________________________________________

______________________________________________________________________

b) Describe how the problem could be avoided.

______________________________________________________________________

______________________________________________________________________

5. Should a sample or a census be used to collect the data?

a) A car manufacturer is switching to a new battery provider.

The manufacturer wants to test the new batteries to make sure

they are reliable in very cold weather.

Would it take a long time to test each battery? ______

Would it cost a lot of money to test each battery? ______

Should a sample or a census be used? __________

b) The Canadian Standards Association wants to survey approximately

2000 people in Alberta who purchased a defective child car seat.

Would it take a long time to survey each person who purchased

a defective car seat? ______

Could using a defective child car seat lead to a serious problem? ______

Is it important that each of the purchasers be notified? ______

Should a sample or a census be used? ___________

6. A sample was used to collect these data. Do you think the conclusions

would be valid? Explain.

To find out if a local swimming pool should extend its hours, all people who

use the pool before noon on weekdays were surveyed.

Do you think most people who use the pool in the morning would care

whether the pool was open later on a night? ______

Do you think the conclusions would be valid? ______

MMS9_Prep book_UnitBM.qxp 7/8/09 4:45 PM Page 377

Page 36

378

9.4 7. Identify the sampling method used for each survey.

a) Ten students from each class are chosen to participate in a survey about

the eating habits of teenagers.

_______________________________________________________________________

_______________________________________________________________________

b) A market researcher wants to find out the favourite brand of sunglasses of

beach goers. He surveys people who walk in front of his deck chair as he

sits on the beach.

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

8. Identify a potential problem with this sampling method.

To find out whether more residents of Vancouver drive an American-made car

or an import, every 5th person entering a Ford dealership was surveyed.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

9. Which sampling method do you think is better? Why?

Martina wants to find out whether residents would like to see more parks built.

Method A: Survey all families with children under 10.

Method B: Randomly survey every 50th person in the local phone book.

Method A: Do families with young children often go to a park? ______

Who do you think is more likely to want more parks built: families

with young children or people without children? ____________________

_________________________________________________________________

Do people with pets often use a park? ______

Is the sample representative of all residents? ______

Method B: Does each resident have an equal chance of being

surveyed? ______

Is the sample representative of all residents? ______

Better method: ____________

MMS9_Prep book_UnitBM.qxp 7/8/09 4:45 PM Page 378

What You’ll Learn

• Understand how probability is used in everyday situations.

• Identify and solve problems related to data collection.

• Use either a population or a sample to answer a question.

• Develop and carry out a plan to collect, display, and analyze data.

343

9

UNIT

Probability and Statistics

Why It’s Important

Probability is used by

• weather forecasters to more accurately predict the weather

• insurance companies to help determine insurance premiums

Key Words

experimental probability

theoretical probability

subjective judgment

assumptions

fair

biased question

census

population

sample

valid conclusions

simple random sampling

systematic sampling

cluster sampling

self-selected sampling

convenience sampling

stratified random sampling

MMS9_Prep book_Unit9.1.qxp 7/8/09 4:42 PM Page 343

Page 2

12% � � 3

25

12

100

Check

1. Write each fraction as a percent.

a) � ________ b) � c) �

� �

� ________ �

2. Write each fraction as a decimal.

a) � ________ b) � ____________ c) � ____________

� ________ � ________

3. Write each percent as a fraction in simplest form.

a) 27% � b) 25% � c) 70% �

� �

� �

100 � 25

100

100

100

3

8

13

50

17

100

100

3

20

2 �

5 � 20

2

5

35

100

9.1 Skill Builder

Relating Fractions, Decimals, and Percents

This hundredths chart represents one whole, 1, or 100%.

The shaded part of this grid can be described in 3 ways.

As a fraction:

As a decimal: 0.16

As a percent: 16%

16

100

Write a fraction as a percent: Write a percent as a fraction:

� 25

� � 75%

� 25

Write a fraction as a decimal:

75

100

3

4

� 1 � 2 � 0.51

2

We can also read as 16 out of 100.16

100

We can think of a

fraction as division.

� 4

� 4

344

MMS9_Prep book_Unit9.1.qxp 7/8/09 4:42 PM Page 344

Page 18

360

The school council wants to know if students would like to have a dance to

celebrate the end of the school year. The council surveys 2 girls from each

grade to find out.

Was a sample or a census used to collect the data?

Do you think the conclusions would be valid? Explain.

Solution

Not all students in the school were surveyed. So, the data were collected from a sample.

All students surveyed were girls. And, 2 students from each grade is probably not enough to

represent the population. So, the conclusions are probably not valid. More students should be

surveyed, with a proportional number of boys and girls included.

Identifying and Critiquing the Use of SamplesExample 3

Check

In each case, was a sample or a census used to collect the data?

Wherever a sample was used, do you think the conclusions would be valid?

Explain.

1. To find out what percent of the population of British Columbia has access to

the Internet, all residents of Victoria were surveyed.

What is the population? ___________________________________

Were all residents surveyed? _______

Was a sample or census used? ____________

Do you think the results of the survey would represent the residents of a small

northern mining community? _______

Do you think the conclusions would be valid? _______

2. To ensure safe and secure air travel from Edmonton International Airport,

anyone boarding a plane at the airport goes through a security check.

What is the population? ________________________________________________

_________________________________________________________________________

Were all people boarding planes checked? _______

Was a sample or a census used? ___________

MMS9_Prep book_Unit9.3.qxd 7/8/09 4:43 PM Page 360

Page 19

361

3. To find out the favourite flavour of bubble tea, every fifth customer of the

bubble tea café is surveyed.

What is the population? ____________________________

Were all customers surveyed? _______

Was a sample or a census used? ____________

Do you think the conclusions would be valid? _______ Why?

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

Practice

1. Identify the population of each survey.

a) The manager of an apartment building wants to find out which apartments

in the building need new carpet.

__________________________________________________________________________________

b) The manager of a video game store in Grande Prairie wants to find out

how many video games are owned by the average teenager in town.

__________________________________________________________________________________

c) A company that manufactures programmable thermostats wants to test its

thermostats for defects.

__________________________________________________________________________________

2. In each case, describe why a sample was used instead of a census.

a) A car company in Canada wants to find out whether people plan to buy or

lease their next vehicle.

__________________________________________________________________________________

__________________________________________________________________________________

b) A clothing manufacturer wants to make sure the guarantee that its clothing

will not shrink when washed is upheld.

__________________________________________________________________________________

__________________________________________________________________________________

MMS9_Prep book_Unit9.3.qxd 7/8/09 4:43 PM Page 361

Page 35

377

9.3

4. Explain why this survey might be problematic.

a) A tourist attraction employs 500 students for the summer. They want to find

out how much money students save from each pay cheque. They plan to

survey each student as he or she is given the next pay cheque.

Is there a problem with time or cost? ______

Is there a problem with privacy? ______

Is there a problem with cultural sensitivity? ______

Explain. _______________________________________________________________

______________________________________________________________________

b) Describe how the problem could be avoided.

______________________________________________________________________

______________________________________________________________________

5. Should a sample or a census be used to collect the data?

a) A car manufacturer is switching to a new battery provider.

The manufacturer wants to test the new batteries to make sure

they are reliable in very cold weather.

Would it take a long time to test each battery? ______

Would it cost a lot of money to test each battery? ______

Should a sample or a census be used? __________

b) The Canadian Standards Association wants to survey approximately

2000 people in Alberta who purchased a defective child car seat.

Would it take a long time to survey each person who purchased

a defective car seat? ______

Could using a defective child car seat lead to a serious problem? ______

Is it important that each of the purchasers be notified? ______

Should a sample or a census be used? ___________

6. A sample was used to collect these data. Do you think the conclusions

would be valid? Explain.

To find out if a local swimming pool should extend its hours, all people who

use the pool before noon on weekdays were surveyed.

Do you think most people who use the pool in the morning would care

whether the pool was open later on a night? ______

Do you think the conclusions would be valid? ______

MMS9_Prep book_UnitBM.qxp 7/8/09 4:45 PM Page 377

Page 36

378

9.4 7. Identify the sampling method used for each survey.

a) Ten students from each class are chosen to participate in a survey about

the eating habits of teenagers.

_______________________________________________________________________

_______________________________________________________________________

b) A market researcher wants to find out the favourite brand of sunglasses of

beach goers. He surveys people who walk in front of his deck chair as he

sits on the beach.

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

8. Identify a potential problem with this sampling method.

To find out whether more residents of Vancouver drive an American-made car

or an import, every 5th person entering a Ford dealership was surveyed.

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

9. Which sampling method do you think is better? Why?

Martina wants to find out whether residents would like to see more parks built.

Method A: Survey all families with children under 10.

Method B: Randomly survey every 50th person in the local phone book.

Method A: Do families with young children often go to a park? ______

Who do you think is more likely to want more parks built: families

with young children or people without children? ____________________

_________________________________________________________________

Do people with pets often use a park? ______

Is the sample representative of all residents? ______

Method B: Does each resident have an equal chance of being

surveyed? ______

Is the sample representative of all residents? ______

Better method: ____________

MMS9_Prep book_UnitBM.qxp 7/8/09 4:45 PM Page 378