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MDM 4U Practice Exam
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Part A. Sampling, Surveying and Analyzing Data
1. Match each term in column A to the correct definition in column B by placing the corresponding
letter in the space beside each term.
15 marks
A
B
Population
A. a measure of the strength of the relationship between two
variables
Frequency
B. the middle value in a data set
Cluster Sampling
C. a data value that does not “fit” into a distribution
Response Bias
D. the shape of a distribution that “tails” to the left or right
Open Question
E. the total number of items or individuals under investigation
Stratified Sampling
F. the width of a distribution
Sample
G. a sampling method where the population is divided into
groups, a number of groups are randomly selected, and all
members of each selected group are sampled
Non-response Bias
H. the middle 50% of data values in a distribution
Median
I. a question that can have an infinite number of responses
Correlation
J. the total number of items or individuals in a given category
Spread
K. the most repeated value in a data set
Outlier
L. the number of items or individuals selected for analysis
Skew
M. an unintended influence on the data that results from failure to
gain responses from all individuals in the sample
Interquartile Range
N. a sampling method where the population is divided into
groups, and members from each group are randomly selected
Mode
O. an unintended influence on the data that results from poor
survey design such as leading questions
2. Explain in words the difference between each of the two terms, and describe an example for each.
(a) quantitative and qualitative
2 marks
(b) discrete and continuous
2 marks
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3. A club of running enthusiasts have been tracking their times when running 1 mile. Their latest
results are shown below in minutes.
7.7, 8.9, 10.4, 6.6, 7.2, 8.3, 9.3, 7.6, 6.2, 8.3, 8.3, 6.1
(a) On the grid provided, plot a histogram of running times.
5 marks
(b) Calculate the mean.
1 mark
(c) Calculate the median.
1 mark
(d) Determine the mode.
1 mark
(e) Given the shape of the distribution, which measure of central tendency should you use and why?
2 marks
(f) Calculate the standard deviation.
3 marks
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MDM 4U Practice Exam
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4. Draw a sketch of each type of distribution, and indicate the location of the mean and median.
6 marks
(a) bimodal
(b) left skew
(c) right skew
5. For each scatterplot shown below:
(i) sketch the line of best fit
(ii) estimate the value of r
(iii) estimate the value of r2
(a)
3 marks
3 marks
3 marks
(b)
(c)
6. Given a normal distribution with 0 = 24.3 and ó = 4.2 calculate:
(a) the percentage of data values greater than or equal to 30
(b) the percentage of data values between 20 and 30
4
2 marks
4 marks
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MDM 4U Practice Exam
7. Refer to the diagram shown below to fill in the blanks that follow.
(a) the mean =
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8 marks
(b) the standard deviation =
(c) range of marks with a z-score of +1 to -1
(d) range of marks with a z-score of ± 2.5
(e) percentage of students with an average of 55% or higher
(f) percentage of students with an average between 55% and 85%
(g) percentage of students with an average of 50% or less
8. The target mass for a box of Cheerios is 300 g. The box is not shipped if its mass has a z-score of
-2.7 or less. Statistical research has shown that the typical standard deviation for the masses of cereal
boxes is 6 g, and is normally distributed.
(a) What must a box of Cheerios weigh in order to be shipped?
2 marks
(b) How many boxes of Cheerios are not shipped if the production line produces 8000 boxes?
5
3 marks
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MDM 4U Practice Exam
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Part B. Theoretical Probability and Probability Distributions
1. State the theoretical probability of the following events. Record as a fraction.
5 marks
(a) drawing a King from a deck of cards
(b) rolling a number higher than 3 on a six-sided die
(c) drawing a diamond or a heart from a deck of cards
(d) rolling anything but a 2 on an eight-sided die
(e) rolling sum of 2 with 2 six-sided dice
2. A bag contains lego blocks. 3 are red, 5 are blue, and 4 are yellow.
(a) What is the probability of drawing a red block on the first draw?
1 mark
(b) What is the probability of drawing a red or a blue block on the first draw?
1 mark
(c) What is the probability of drawing a red block followed by a blue block (the red block is not
returned)?
2 marks
(d) What is the probability of not drawing a yellow block?
1 mark
3. If two six-sided dice are rolled, one red and the other blue, find the probability of rolling a sum of 4 or
a pair. (You may want to draw an outcome table).
4 marks
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4. In a study of 20 000 patients, 12 000 were male and 8000 were female. 5000 males were smokers and
5000 females were smokers. 1000 males and 1200 females died from lung cancer. 800 of the males who
died of lung cancer were smokers, and 1000 of the females who died of lung cancer were smokers.
(a) Organize the above information in the table shown below
Smoker
Die Lung
Cancer
4 marks
Non-Smoker
Did Not Die
Die Lung
Cancer
Did Not Die
Total
Males
Females
Total
Using the information in your outcome table determine:
8 marks
(a) P(smoker# female)
(b) P(smoker# male)
(c) P(dying from lung cancer# male)
(d) P(dying from lung cancer# male# smoker)
(e) P(dying from lung cancer# female)
(f) P(dying from lung cancer# female# smoker)
(g) Which gender is more likely to smoke?
(h) Which gender is more likely to die of lung cancer if they smoke?
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5. A survey of 100 Grade 9 students produced the following results.
Sport Played
Number of Students
Basketball
30
Volleyball
30
Soccer
40
Basketball
and
Volleyball
16
Volleyball
and Soccer
14
Basketball
and Soccer
10
All three
sports
6
(a) Draw a Venn diagram to represent the results shown in the table.
5 marks
(b) What is the probability of a student playing only Basketball?
1 mark
(c) What is the probability of a student playing only Volleyball or only Soccer?
2 marks
(d) What is the probability of a student playing Volleyball, given that they play Soccer?
2 marks
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6. Perform the following calculations.
(a) 5!3!
2!2!
3 marks
(b) P(10, 3)
(c) 12C7
7. Explain the difference between the number of combinations and the number of permutations. 2 marks
8. A goalie has a success rate of 80% for saves. Calculate the probability of each of the following:
(a) He saves three pucks out of five shots on net
3 marks
(b) He lets in 5 shots in a row
3 marks
(c) He saves the first two shots but lets the next three in
3 marks
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MDM 4U Practice Exam
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9. A volleyball team has ten players. To play a game, 6 players are needed to play positions numbered
from 1 to 6.
(a) How many different combinations of 6 players can the coach choose from to play a game?
1 mark
(b) How many different line ups of 6 players (where order matters) can the coach choose from to play a
game?
1 mark
(c) If Julie and Abby are the team’s best players and are always played in positions 2 and 5, how many
different line ups are possible?
2 marks
(d) The four best players are always played in the same positions. This leaves two positions for the
remaining team members. If every remaining team member has an equal chance of being selected and
can play in either of the two positions, what is the probability they will be chosen to play?
3
marks
10. Determine each of the following.
(a) Expand and simplify (x + w)5.
3 marks
(b) the 5th term of (2s + 3)12
2 marks
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11. A multiple choice quiz has 5 questions. There are 4 possible answers to choose from for each
question.
(a) What is the probability you will get any given question correct?
1 mark
(b) What is the probability you will get any given question wrong?
1 mark
Quiz
Scores
(X)
Theoretical
Probability
P(X)
(c) Determine the probability distribution for quiz scores of 0 to 5 out
of 5.
5 marks
(c) Determine the probability of getting 3 or less questions right.
1 mark
(d) Determine the probability of getting all 5 questions right.
1 mark
(e) Determine the probability of getting two or less questions right.
1 mark
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MDM 4U Practice Exam
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12. Jim and Jane hope to have six children. If the probability of having a boy or a girl is equal, determine
the probability of each scenario.
(a) that four of the children will be boys
2 marks
(b) that at least two of the children will be girls
2 marks
(c) that all six children will be girls
2 marks
13. An airline has determined that 4% of people do not show up for their flights. To avoid having empty
seats, airlines over-book. A jet that is flying to Paris holds 300 people.
(a) What is the probability that some travelers will not get a seat if 310 seats are sold?
(b) How many tickets could be oversold in order to be 95% sure that everyone will get a seat?
12
3 marks
3 marks