Download MATH 9 CHAPTER 11 ASSIGNMENT PROBABILITY AND

MATH 9
CHAPTER 11 ASSIGNMENT
PROBABILITY AND STATISTICS
Show ALL work for the required questions. Do NOT assume that I will know what you
mean.
1. Choose from the following terms to complete each sentence. Use your notes to help you.
(4 marks)
bias
ethics
influencing factors
survey
biased sample
generalize
experimental
theoretical
a. A ___________________can be used to collect opinions and/or information about a
topic.
b. If a sample represents the population, you can ____________________ the results to
the population.
c. Several __________________________ affect how data are collected or how responses
are obtained.
d. You can use ____________________probability and ____________________
probability to help make decisions based on probability.
e. An influencing factor that shows a preference for a specific product is an example of
____________________.
f. A ______________________ can make survey results inaccurate.
g. An influencing factor that involves judgements of right and wrong is an example of
____________________.
2. Write an appropriate survey question for each situation that will collect helpful data. Also,
identify whom you would ask to participate in the survey. (2 marks)
a. You want to find out which music group teens like best.
i. Question –
ii. Whom to ask –
3. In each case, identify and describe any influencing factors that may affect the collection of
data. (Identify – 1 mark; Describe – 1 mark = 10 marks)
a. A sales representative e-mails a survey to you. In exchange for your participation,
you will have a chance to win a trip for two people to a destination you choose.
There is no other information.
b. An interest group surveys community residents about whether or not they would
support a curfew for teens. The survey is being conducted the week after several
incidents of vandalism at the high school were reported in the newspaper.
c. The coach of a baseball team needs drivers with good safety records to transport
players to tournaments. She asks each parent at a parent meeting if they had any
traffic violations in the last six months.
d. Ask Grade 9 students if they would use a cell phone in class, even though it is not
allowed.
e. An information package and survey are mailed to 3000 residents about a proposal to
improve the gardens in the local park. The cost to print and mail each survey is $10.
4. Rewrite the survey question so that it collects more helpful data. (1 mark)
Is lacrosse your favorite sport?
5. For each situation, develop a survey question that is clearly written and free from influencing
factors. (1 mark each)
a. A teacher wants to know which Internet browser is most popular with students.
b. A cell phone company wants to know whether to offer free message manager or free
texting for their new promotional package.
6. Match the following statement with the related type of sample. (5 marks)
___ All of the people leaving a concert are handed a card and
asked to mail in their response.
a. convenience sample
___A food services company surveys 10% of the students at
each of four high schools in the district.
b. random sample
___Every tenth person on a voter’s list is polled about whom
they will vote for in the next election.
c. stratified sample
___Franco surveyed all of his friends about their favorite pastime.
d. systematic sample
___At the mall, a marketing representative asks customers
chosen at random about which grocery store they prefer.
e. voluntary response
Sample
7. There are 1400 students enrolled at the school. Anya suggests using a random sample of 30
students. Lara suggests using a stratified sample to get input from each grade. Ian wants to
survey the whole student population.
a. Whose sampling method is better? Why? (2 marks)
b. Explain why the other two sampling methods are not appropriate. (2 marks)
8. For each situation:
 Identify the population. (1 mark each)
 Decide if you would survey the population or a sample. Justify your choice.
(2 marks each)
a. Determine the reliability of a new cell phone.
b. Determine the games that Grade 9 students want to play at a winter carnival.
c. Determine which style of jacket the members of a Hunters and Trappers Association
prefer.
d. Determine how many people would use a library in a new subdivision.
9. A city council wants to survey residents about building a new water treatment plant. For
each survey:
 Identify the type of sample. (1 mark each)
 Describe how the survey could be set up. (2 marks each)
 Explain whether the results would accurately represent the population. (1 mark)
a. The council plans to survey 1000 residents. The city has 50 000 residents who own
their own home, 10 000 residents who own their condominium, 30 000 residents
who rent apartments, and 10 000 residents who rent homes.
b. A councillor plans to survey all the residents who own homes in her area of the city.
c. The council plans to survey residents using a list of names in the phone book.
d. The council plans to set up a poll at the four grocery stores in the city and survey 100
people at each store.
10. A manufacturer makes the following claim about the lifetime of its batteries.
Each battery has a lifetime of 100 hours.
Carla and Pedro tested 20 batteries to check the claim. Five batteries lasted less than 100
hours and two batteries lasted exactly 100 hours. The rest lasted longer than 100 hours.
The students predicted that 25% of the batteries made by the company would not meet the
claim.
a. Did the sample lead the students to make a false prediction? Explain. (2 marks)
b. If the prediction is false, explain what you would change to make the prediction more
accurate. (1 mark)
11. A school with 5400 students is electing a student council president. A reporter for the
student newspaper polled 100 people. The table shows that 45% chose candidate A, 15%
chose candidate B, and the rest chose candidate C.
a. According to the poll, how many students will choose each candidate? (2 marks)
Candidate Candidate
A
B
45%
15%
Candidate
C
Total
100%
5400
b. What is the experimental probability for candidate C? (1 mark)
c. What is the theoretical probability that a voter will choose candidate C? (1 mark)
d. What assumption did you make? (1 mark)
e. The reporter predicts that candidate C will win the election. Do you agree with her
prediction? Explain your reasoning. (2 mark)
12. Cody records the scores from his ten most recent golf games.
Game
1
2
3
4
5
6
7
8
9
10
Score
70
69
71
73
74
72
73
75
78
74
a. Calculate Cody’s mean score based on all ten games. (1 mark)
b. Use the first three game scores as a sample. Calculate the mean. (1 mark)
c. Use the last three game scores as a sample. Calculate the mean to the nearest hundredth.
(1 mark)
d. Compare the mean from each sample to the mean for all games. Are the samples a good
predictor for Cody’s overall score? Explain. (2 marks)
13. The students of a local high school operate the canteen at school to raise funds for new
furniture in the student lounge. Average sales of $245 per month are needed to reach the
goal. The sales for the first three months were $190, $245 and $210. Since the sales appear
to be too low, the students predict that they will not reach their goal.
a. What were the average sales for the first three months, to the nearest dollar?
(1 mark)
b. Using all the sales (as listed in the table below), was the student’s prediction correct?
Explain. (2 marks)
Month
Sales
Sept
190
Oct
245
Nov
210
Dec
350
Jan
265
Feb
325
Mar
305
Apr
225
May
265
June
300
14. Cal randomly surveys 100 students about their favorite subject. There are 500 students in
the school. The table displays the results.
Subject
Total
Math
30
English History Science
35
13
22
a. What is the theoretical probability that a student will choose math? (1 mark)
b. What assumptions did you make? (1 mark)
c. Based on the survey results, predict how many of the 500 students prefer math. Show
your calculations. (2 marks)
d. Compare the theoretical probability and the experimental probability. Explain any
differences. (2 marks)