Download Chapter 5 Review

Math 20 Foundations Review
Name: _____________________
Chapter 1:
Multiple choice:
1. Emma works part time at a bakery shop in Saskatoon. Today, the baker made 20 apple pies, 20 cherry pies,
and 20 bumbleberry pies. What conjecture is Emma most likely to make from this evidence?
a. People are more likely to buy bumbleberry pie than any other pie
b. People are more likely to buy apple pie than any other pie
c. Each type of pie will sell equally as well as the others
d. People are more likely to buy cherry pie than any other pie
2. Justin gathered the following evidence:
17(22) = 374
14(22) = 308
36(22) = 742
18(22) = 396
Which conjecture, if any, is Justin most likely to make from this evidence?
a. When you multiply a two-digit number by 22, the last and first digits of the product are the digits of
the original number.
b. When you multiply a two-digit number by 22, the first and last digits of the product are digits of the
original number.
c. When you multiply a two-digit number by 22, the first and last digits of the product form a number
that is twice the original number.
d. None of the above conjectures can be made from this evidence.
3. Which conjecture, if any, could you make about the product of an odd integer and an even integer?
a. The product will be an even integer.
b. The product will be an odd integer.
c. The product will be negative.
d. It is not possible to make a conjecture.
4. Jason created the following table to show a pattern.
Multiples of 27
54
81
108
135
Sum of the Digits
9
9
9
9
Which conjecture could Jason make, based solely on this evidence? Choose the best answer.
a. The sum of the digits of a multiple of 27 is equal to 9.
b. The sum of the digits of a multiple of 27 is an odd integer.
c. The sum of the digits of a multiple of 27 is divisible by 9.
d. Jason could make any of the above conjectures, based on this evidence.
5. Sasha made the following conjecture:
All polygons with six equal sides are regular hexagons.
Which figure, if either, is a counterexample to this conjecture? Explain.
a.
b.
c.
d.
Figure A is a counterexample, because all six sides are equal and it is a regular hexagon.
Figure B is a counterexample, because all six sides are equal and it is a regular hexagon.
Figure B is a counterexample, because all six sides are equal and it is not a regular hexagon.
Figure A is a counterexample, because all six sides are equal and it is not a regular hexagon.
162
9
6.
Randolph made the following conjecture: The sum of a multiple of 4 and a multiple of 8 must be a multiple
of 2. Which choice, if either is a counterexample to this conjecture?
1. 4 + 8 = 12
2. 8 + 8 = 16
a. Choice 2 only
b. Choice 1 and choice 2
c. Choice only
d. Neither choice 1 nor choice 2
7. Pearl made the following conjecture: The sum of a multiple of 4 and a multiple of 8 must be a multiple of 8.
Is the following equation a counterexample to this conjecture? Explain.
24 + 24 = 48
a.
b.
c.
d.
No, it is not a counterexample, because 48 is not a multiple of 8.
No, it is not a counterexample, because 48 is a multiple of 8.
Yes, it is not a counterexample, because 48 is not a multiple of 8.
Yes, it is not a counterexample, because 48 is a multiple of 8.
8. Bob made the following conjecture: The difference between two numbers always lies between the two
numbers.
Is the following equation a counterexample to this conjecture? Explain.
6 – (-2) = 8
a.
b.
c.
d.
Yes, it is a counterexample, because 8 lies between -2 and 6.
No, it is not a counterexample, because 8 lies between -2 and 6.
No, it is not a counterexample, because 8 is greater than -2 and 6.
Yes, it is a counterexample, because 8 is greater than -2 and 6.
9. All alligators are reptiles. All reptiles are covered with scales. Tashi is a reptile. What can be deduced about
Tashi?
1. Tashi is an alligator
2. Tashi has scales
a. Choice 2 only
b. Choice 1 and choice 2
c. Choice only
d. Neither choice 1 nor choice 2
10. Which of the following choices, if any, uses inductive reasoning to show that the sum of two odd integers is
even?
a. (2x + 1) + (2y + 1) = 2(x + y + 1)
b. 2x + 2y + 1 = 2(x + y) + 1
c. 3 + 5 = 8 and 7 + 5 = 12
d. None of the above choices
11. Which of the following choices, if any, uses deductive reasoning to show that the sum of two odd integers is
even?
a. (2x + 1) + (2y + 1) = 2(x + y + 1)
c. 3 + 5 = 8 and 7 + 5 = 12
b. 2x + 2y + 1 = 2(x + y) + 1
d. None of the above choices
12. What type of error, if any, occurs in the following deduction?
All people drive cars to work.
Gavin drives to work.
Therefore, Gavin drives a car.
a.
b.
c.
d.
A false assumption or generalization
An error in reasoning
An error in calculation
There is no error in the deduction
13. Which type of reasoning does the following statement demonstrate?
Every multiple of 9 has a factor of 3.
27 is a multiple of 9.
Therefore, 27 has a factor of 3.
a. Inductive reasoning
b. Deductive reasoning
c. Neither inductive nor deductive reasoning
14. Choose the next figure in the sequence:
15. Emma and Alexander are playing darts. Emma has a score of 37. To win, she must reduce her score to zero
and have her last counting dart be a double. Which of the following scores on the dart board, in order, would
give her the win?
a. 15, 16, 6
b. 8, 7, double 10
c. Double 11, 6, 9
d. 9, 6, double 11
Short Answer:
16. What conjecture could you make about the product of two odd integers and one even integer?
17. Adam made the following conjecture:
The sum of a multiple of 7 and a multiple of 8 will be an even number.
Do you agree or disagree? Briefly justify your decision with a counterexample if possible.
18. Prove, using deductive reasoning, that the product of an odd integer and an odd integer is always odd.
19. What type of error occurs in the following deduction? Breifly justify your decision.
Let x = y
x2 = xy
x2 + x2 = x2 + xy
2x2 = x2 + xy
2
2x – 2xy = x2 + xy – 2xy
2x2 – 2xy = x2 – xy
2(x2 – xy) = 1(x2 – xy)
2=1
20. What type of error occurs in the following deduction? Breifly justify your answer.
3=3
7(3) = 7(2 + 1)
7(3) + 6 = 7 (2 + 1) + 6
21 + 6 = 14 + 7
27 = 21
21. Does the following statement demonstrate inductive reasoning or deductive reasoning?
Every Monday afternoon at 6:00 p.m., the news is broadcast on television. Today is Monday, therefore, the
news will be broadcast on television.
22. Does the following statement demonstrate inductive reasoning or deductive reasoning?
All reptiles have scales. Crocodiles are reptiles. Therefore, crocodiles have scales.
23. The square of an odd integer is subtracted from the square of an odd integer. Develop a conjecture about
whether the difference is odd or even. Provide evidence to support your conjecture.
24. Bill made the following conjecture:
When you add a multiple of 6 and a multiple of 9, the sum will be a multiple of 6.
Isabelle disagreed with Bill’s conjecture, however, because 24 + 27 = 51, and 51 is not a multiple of 6. How
could Bill’s conjecture be improved? Explain the changes you would make.
25. Blake discovered a number trick in a book he was reading:
Choose a number.
Subtract 2.
Multiply by 3.
Add 9.
Multiply by 3.
Subtract 9.
Divide by 9.
Prove deductively that any number you choose will be the final result.
26. Alexandra, Morana, Rebecca and Yvonne play on the high school basketball team. After the first quarter of
one game, Morana led Rebecca by 3 points. Yvonne led Alexandra by 5 points, and Rebecca led Alexandra by
2 points. In the second half, Alexandra got 4 points while Rebecca was scoreless. At half time, Yvonne was
ahead of Morana by 4 points and Morana was 4 points ahead of Rebecca. Morana, Yvonne, and Rebecca did
not play in the second half of the game. At the end of the game, Alexandra had 2 more points than Yvonne.
Who finished third in scoring?
Chapter 2:
Multiple choice:
1. Which pairs of angles are equal in this diagram?
a.
b.
c.
d.
b = e, c = h, and d= g
b = a, c = e, and d=f
b = c, e=g, and f=h
b=f, c=g, and d=h
a.
b.
c.
d.
Alternate exterior angles
Supplementary angles
Alternate interior angles
Corresponding angles
a.
b.
c.
d.
w = 146o, x = 44o, y = 146o
w = 134o, x = 46o, y = 46o
w = 136o, x = 44o, y = 136o
w = 116o, x = 64o, y = 64o
a.
b.
c.
d.
YXZ= 52o,
YXZ= 52o,
YXZ= 62o,
YXZ= 62o,
2. In which diagrams is AB parallel to CD?
a.
b.
c.
d.
Choice 2 only
Choice 1 and choice 2
Choice only
Neither choice 1 nor choice 2
3. Which angle property proves BED = 73O
4. Which are the correct measures of the indicated angles?
5. Which are the correct measures for YXZ and XZY?
XZY= 77o
XZY= 87o
XZY= 77o
XZY= 87o
6. Which are the correct measures for KLM, KLN, NML?
a.
b.
c.
d.
KLM= 117o, KLN= 36o, NML=124o
KLM= 71o, KLN= 24o, NML=63o
KLM= 73o, KLN= 67o, NML=117o
KLM= 63o, KLN= 28o, NML=117o
7. Which are the correct measures for WXZ, UZY, VYX?
a.
b.
c.
d.
WXZ and UZY cannot be determined; VYX = 120o
WXZ, UZY and VYX cannot be determined
WXZ cannot be determined; UZY = 120o, VYX = 120o
WXZ =120o, UZY = 120o, VYX = 120o
Short Answer:
8. Determine the measure of  PQT and PQR.
9. Determine the sum of the measures of the interior angles of this nine sided polygon. Show your calculation.
10. Each interior angle of a regular convex polygon measures 156o. How many sides does the polygon have?
11. Determine the value of b and c.
Chapter 3/4:
Multiple choice:
1. Solve for the unknown side length. Round your answer to one decimal place.
𝑡
3.5
=
sin 58° sin 47°
a. 4.1
c. 5.6
b. 4.7
d. 5.1
2. Solve for the unknown angle measure. Round your answer to the nearest degree.
15.2
12.0
=
sin 𝐻 sin 50°
a. 75o
c. 76o
b. 77o
d. 74o
3. What information do you need to know about an acute triangle to use the sine law?
a. Two angles and any side
c. All the angles
b. Two sides and any angle
d. All the sides
4. How would you determine the indicated angle measure, if it is possible?
a.
b.
c.
d.
The sine law
Not possible
Primary trigonometric ratios
The cosine law
5. Which one of the following equations is valid?
a. cos 36o = -cos 144o
b. cos 36o = -cos 36o
c. cos 36o = cos 144o
d. none of the above
6. Which law could you use to determine the unknown angle in this triangle?
a. the sine law and the cosine law
b. The sine law only
c. Neither the sine law nor the cosine law
d. The cosine law only
7. Which set of measurements can produce two possible triangles?
a. A = 28O, a = 10.5 m, b = 15.0 m
c. A = 28O, a = 16.0 m, b = 15.0 m
b. A = 28O, a = 7.0 m, b = 15.0 m
d. A = 28O, a = 5.5 m, b = 15.0 m
8. In ∆XYZ, Y = 29o, x = 15.4 m, and y = 12.0 m.
Which statement is true for this set of measurements?
a. This is not a SSA situation
b. This is a SSA situation; no triangle is possible.
c. This is a SSA situation; only one triangle is possible.
d. This is a SSA situation; two triangles are possible.
9. In ∆JKL, J = 115o, k = 6.2 m, and j = 5.5 m.
Which statement is true for this set of measurements?
a. This is not a SSA situation
b. This is a SSA situation; no triangle is possible.
c. This is a SSA situation; only one triangle is possible.
d. This is a SSA situation; two triangles are possible.
10. In ∆CDE, D = 59o and DE = 9.0 cm.
What is the height of the triangle from base DC?
a. 6.8 cm
b. 7.1 cm
c. 7.4 cm
d. 7.7 cm
11. Determine the indicated angle measure to the nearest degree.
a.
b.
c.
d.
98o
100o
102o
Cannot be determined
Short Answer:
12. Sketch a triangle that corresponds to the equation. Then determine the third angle measure and the third
side length.
25.0
32.0
=
sin 45° sin 65°
13. Determine the measure of a to the nearest degree.
14. In ∆QRS, r = 4.1 cm, s = 2.7cm, and R = 88o. Determine the measure of Q to the nearest degree.
15. Determine the measure of a to the nearest degree.
16. In ∆DEF, d = 12.0cm, e = 10.8cm, and f = 12.4cm. Determine the measure of D to the nearest degree.
17. In ∆ABC, A = 58o, a = 10.5cm, and b = 11.4cm. Determine the number of triangles (zero, one or two) that
are possible for these measurements. Draw the triangle(s) to support your answer.
18. In ∆UVW, U = 87o, u = 13.8cm, and v = 7.9cm. Does this involve the SSA situation? If so, how many triangles
with the given measurements are possible? Draw the triangle(s) to support your answer.
19. Determine the indicated side length to the nearest tenth of a centimeter.
20. Determine to the nearest centimeter, the perimeter of the triangle. Show your work.
21. In ∆MNO, N = 43o, NO = 12.4cm.
Calculate the height of the triangle from base NM, to the nearest tenth of a centimeter. Determine the
possible lengths of side OM, so that there are zero, one or two triangles that satisfy these conditions. Draw
each triangle to support your answer.
Chapter 6
Multiple Choice:
1. What is the boundary line for the linear inequality 2x + 2y < 16?
a.
y=8–x
c.
b.
x=8–y
d.
2. Which test point is in the solution set for the linear inequality
{(x, y) | x + y < 3, x W, y W}?
a.
(1, 1)
b.
(–2, 5)
c.
(2, 2)
y = 16 – x
y = 4 – 2x
d.
3. How would you graph the solution set for the linear inequality 4y – 2x < 20?
a.
Draw a dashed boundary line y = x + 10, then shade above the line.
b.
Draw a dashed boundary line y = x + 10, then shade below the line.
c.
Draw a solid boundary line y = x + 10, then shade below the line.
d.
Draw a solid boundary line y = x + 10, then shade above the line.
4. What system of linear inequalities is shown here?
y
a.
5
4
b.
3
2
c.
1
–5
–4
–3
–2
–1
–1
–2
–3
1
2
3
4
5
x
d.
x – y –2
y x
x–y 2
y x
x+y 2
y x
–x + y –2
y x
–4
–5
5. Which test point is in the solution set for the following system of linear inequalities?
{2y – 6x < 12, 4x + 4y 0, x I, y I}
a.
(1, 2)
c.
(–10, 0)
b.
(2, –1)
d.
(–1, –1)
6. A football stadium has 60 000 seats.
• 70% of the seats are in the lower deck.
• 30% of the seats are in the upper deck.
• At least 40 000 tickets are sold per game.
• A lower deck ticket costs $100, and an upper deck ticket costs $60.
Let x represent the number of lower deck tickets.
Let y represent the number of upper deck tickets.
What are the restrictions on x and y?
a.
b.
x ∈ W, y ∈ W
x ∈ I, y ∈ I
c.
d.
x ∈ R, y ∈ R
No constraints.
7. A football stadium has 60 000 seats.
• 70% of the seats are in the lower deck.
• 30% of the seats are in the upper deck.
• At least 40 000 tickets are sold per game.
• A lower deck ticket costs $100, and an upper deck ticket costs $60.
Let x represent the number of lower deck tickets.
Let y represent the number of upper deck tickets.
How would you write the objective function for revenue, R?
a.
R = 70y + 30x
c.
R = 70x + 30y
b.
R = 100x + 60y
d.
R = 100y + 60x
8. A vending machine sells juice and pop.
• The machine holds, at most, 200 cans of drinks.
• Sales from the vending machine show that at least 3 cans of juice are sold for each can of
pop.
• Each can of juice sells for $1.50, and each can of pop sells for $1.00.
Let x represent the number of cans of pop.
Let y represent the number of cans of juice.
Which of the following is a constraint of this optimization problem?
a.
x + y 200
c.
2x + y 200
b.
x + y 200
d.
x + 2y 200
9. Which point in the model below would result in the maximum value of the objective function
10x?
W = 5y –
y
a.
b.
c.
d.
5
B
4
3
D
2
A
–5
–4
–3
–2
C
1
–1
–1
B (1, 4)
C (4, 1)
A (–2, 1)
D (1, 2)
1
2
3
4
5
x
–2
–3
–4
–5
Short Answer:
10. Which side of the boundary line is the solution set for the linear inequality x + 2y – 1 > 0?
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
11. Graph the system of linear inequalities:
{(x, y) | x + y 2, x > –3, x R, y R}
12. Graph the system of linear inequalities:
{(x, y) | x + y 2, x > –3, x W, y W}
13. A Saskatchewan farmer is planting corn and barley.
• He wants to plant no more than 800 ha altogether.
• The farmer wants at least four times as many hectares of barley as corn.
• The yield per hectare of corn averages 60 bushels, and the yield per hectare of barley
averages 30 bushels.
• Corn pays the farmer $7 per bushel, and barley pays $4 per bushel.
Let b represent the number of hectares of barley.
Let c represent the number of hectares of corn.
1. Describe any restrictions on the variables.
2. Write the objective function to determine the combination of corn and barley that will result in the
maximum profit.
3. Write a linear inequality to represent the first point above.
4. Write a linear inequality to represent the second point above.
5. List 2 points in the feasible region
14. Which point in the model below would result in the maximum value of the objective function
y? What is the value of K at this optimal solution?
y
3
2
1
1
2
3
x
K = 5x –
15. The following model represents an optimization problem. Determine the maximum solution.
Restrictions:
x W
y W
Constraints:
x>0
y>0
5x y + 5
x + y 25
Objective function:
A = x + 2y
16. Gordon’s favourite activities are going to the movies and skating with friends. He budgets himself no more
than $180 a month for entertainment and transportation. Movie admission is $12 per movie, and skating
costs $10 each time. A student bus pass for the month costs $50.
a) Define the variables and write a linear inequality to represent the situation.
b) Graph the linear inequality. Use your graph to determine:
i.
a combination of activities that Gordon can afford with no money left over
ii.
a combination of activities that will exceed his budget
Chapter 7 Review:
Multiple Choice:
1. Which description of a graph appears to represent a quadratic relation?
a. a line straight up and down
c. a parabola opening up
b. an ellipse
d. a parabola opening to the right
2. Which relation is quadratic?
a. y = x2 – x2 + 4x + 2
b. y = (2x2)(x + 1)
c. y = (x + 5)2
d. y = 2x – 6x + 3
3. Which parabola opens upward?
a. y = 2x – 4x2 – 5
b. y = 2 + 4x – 5x2
c. y = 4 – 2x2 –5x
d. y = –5x + 4x2 + 2
y
4. Which set of data is correct for this graph?
5
4
A.
Axis of
Symmetry
x = –2
Vertex
Domain
Range
(–0.25, –3.125)
x∈R
y∈R
B.
x = –0.25
(–0.25, 3.125)
x∈R
y ≤ 3.125
C.
x = –0.5
(–0.5, 3)
–2.5 ≤ x ≤ 1.5
Y≤3
D.
x=3
(3, –0.5)
–3 ≤ x ≤ 2
y≤5
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
–2
–3
–4
–5
5. The points (–1, 14) and (9, 14) are located on the same parabola. What is the equation for the axis of
symmetry for this parabola?
a. x = 7
c. x = –4.5
b. x = 4
d. x = 5
y
6. What is the correct quadratic function for this parabola?
5
4
3
a.
b.
c.
d.
f(x) = (x – 1)(x + 3)
f(x) = (x + 1)(x + 3)
f(x) = –(x + 1)(x – 3)
f(x) = (1 – x)(3 – x)
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
–2
–3
–4
–5
7. Which relation is the factored form of f(x) = –3x2 – 3x + 9?
a. f(x) = 3(x + 2)(1 – x)
c. f(x) = (3x – 3)2
d.
b. f(x) = –3(x + 2)(x + 1)
f(x) = –3(x + 3)2
5
x
x
Short Answer:
8. Fill in the table for the relation y = –x2 – 4x + 12.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
9. Determine the roots of the corresponding quadratic equation for the graph.
10. A quadratic function has an equation that can be written in the form f(x) = a(x – r)(x – s). The graph of the
function has x-intercepts at (3, 0) and (6, 0) and passes through the point (7, –4). Write the equation of the
function.
11. Fill in the table for the quadratic function f(x) = –2(x + 5)(x + 2).
y-intercept
Zeros
Axis of symmetry
Vertex
12. Use the graph to determine the equation of the parabola.
1
–2
–1
y
1
2
x
–1
–2
–3
13. For the quadratic function f(x) = –2x2 + 6x + 12:
a. Use a partial factoring strategy to determine two points that are the same distance
from the axis of symmetry.
b. Determine the coordinates of the vertex.
c. Sketch the graph.
Chapter 5 Review:
Multiple choice:
1. Determine the range of the following test scores.
History Test 1 Scores (out of 100)
90
84
77
66
89
84
77
65
86
82
75
65
86
81
72
61
84
79
70
56
a.
b.
c.
d.
90
34
56
78
2. Determine the mean of the following test scores.
History Test 1 Scores (out of 100)
90
84
77
66
89
84
77
65
86
82
75
65
86
81
72
61
84
79
70
56
a.
b.
c.
d.
76.45
79.2
78.5
74.25
3. Determine the median of the following test scores.
History Test 1 Scores (out of 100)
90
84
77
66
89
84
77
65
86
82
75
65
86
81
72
61
84
79
70
56
a.
b.
c.
d.
56
79
78
77
4. Environment Canada recorded the amount of rain (in millimetres) in Jasper, AL for two months.
0
0
0
3.8
9.0
0
0
What value goes in the first row of this frequency
0
0
0
0
0
0
7.4
table?
0.2
0
1.2
0
2.2
0
Precipitation
0
0
6.4
2.0
4.6
0
(mm)
Frequency
0
1.0
0
1.2
0
0
0–1.9
0
0.4
0
3.4
0
1.6
2.0–3.9
5
0
0
0
0
1.2
5.0
4.0–5.9
4
0
1.4
0
0
0.2
7.2
6.0–7.9
3
1.4
4.6
0
5.8
1.2
0
8.0–9.9
1
0
0
0
3.2
0.6
0
a. 51
b. 49
c. 48
d. 50
5. Environment Canada compiled data on the number of lightning strikes per square kilometre in Alberta and
British Columbia towns from 1999 to 2008.
0.42 0.04 0.81 0.40 0.03 0.74
0.28 0.03 0.70 0.23 0.03 0.66
0.13 0.02 0.61 0.12 0.01 0.58
0.10 0.00 0.49 0.07 1.08 0.43
0.05 0.91 0.42 0.04 0.88
Which range of data occurs most frequently?
a. 0.20–0.39
b. 0.40–0.59
c. 0.60–0.79
d. 0.80–0.99
6. Which histogram represents the following test scores?
Geography Test 2 Scores (our of 100)
94
85
77
67
54
93
83
72
64
52
90
83
72
64
48
88
81
70
62
45
86
80
68
59
45
a.
b.
c.
d.
7. Environment Canada compiled data on the number of lightning strikes per square kilometre in Alberta and
British Columbia towns from 1999 to 2008.
0.42 0.04 0.81 0.40 0.03 0.74
0.28 0.03 0.70 0.23 0.03 0.66
0.13 0.02 0.61 0.12 0.01 0.58
0.10 0.00 0.49 0.07 1.08 0.43
0.05 0.91 0.42 0.04 0.88
Determine the mean, to two decimal places.
a. 0.12
b. 0.00
c. 0.36
d. 0.60
8. A set of data is normally distributed. What percent of the data is within two standard deviation of the mean?
a. about 68%
c. about 50%
b. 100%
d. about 95%
9. The ages of participants in a bonspiel are normally distributed, with a mean of 40 and a standard deviation of
10 years. What percent of the curlers are between 40 and 50?
a. 95%
b. 34%
c. 16%
d. 68%
10. A teacher is analyzing the class results for a physics test. The marks are normally distributed with a mean (µ) of
76 and a standard deviation (σ) of 4.
Determine Guy’s mark if he scored µ + 2 σ.
a. 80
c. 84
b. 72
d. 68
11. Which set is normally distributed?
Interval
0–9
10–19
Set A.
2
5
Set B.
5
5
Set C.
1
5
Set D.
8
9
a. Set A.
b. Set B.
20–29
7
4
9
3
30–39
10
5
10
11
12. Determine the z-score for the given value.
µ = 52, σ = 6, x = 64
a. –2
b. 0.5
40–49
15
5
4
8
c. Set D.
d. Set C.
50–59
15
0
1
14
c. –0.5
d. 2
13. Determine the percent of data to the left of the z-score: z = 1.44.
a. 94.95%
c. 93.82%
b. 95.91%
d. 92.51%
14. Determine the percent of data between the following z-scores:
z = –1.50 and z = 1.50.
a. 47.20%
b. 100%
Short Answer:
15. Joel researched the average daily temperature in his town.
Average Daily Temperature in Lloydminster, SK
Month
Jan. Feb. Mar. Apr. May Jun. Jul.
average daily
–
–17.5 –5.0 3.7
10.7 14.3 20.1
temperature (°C)
10.0
c. 94.41%
d. 88.82%
Aug.
14.0
Sep.
9.8
Oct.
4.8
Nov.
–5.8
Dec.
–14.8
a. Determine the mean of the data to the nearest tenth of a degree.
b. Determine the median of the data to the nearest tenth of a degree.
16. Environment Canada compiled data on the number of lightning strikes per square kilometre in Ontario
towns from 1999 to 2008.
3.60 2.11 0.96 0.65
Lightning
3.47 2.04 0.90 0.65
Strikes (per
2.53 1.90 0.85 0.65
square
Frequency
2.38 1.90 0.72 0.63
kilometre)
2.25 1.33 0.70 0.38
0.00–0.99
2.25 1.13 0.66 0.19
1.00–1.99
2.00–2.99
Complete the frequency table:
3.00–3.99
17. Why are frequency polygons better for comparing multiple sets of data than histograms?
18. Khamid and Gerbrand are laying interlocking bricks. Their supervisor records how many bricks they lay
each hour.
Hour
1
2
3
4
5
6
Khamid
212
193
204
195
182
216
Gerbrand
230
195
214
207
218
191
Which worker is more consistent? (calculate σ)
19. The ages of members in a hiking club are normally distributed, with a mean of 32 years and a standard
deviation of 6 years. What percent of the members are between 32 and 44?
20. Determine the z-score for the given value.
µ = 9.3, σ = 0.4, x = 8.8
21. Determine the percent of data to the right of the z-score: z = –0.68.
22. Determine the percent of data between the following z-scores:
z = –2.99 and z = 1.50.
23. In a population, 80% of the adults are taller than 165 cm and 20% are taller than 187 cm. Determine the
mean height and standard deviation for this population.
24. A manufacturer of plasma televisions has determined that the televisions require servicing after a mean of
62 months, with a standard deviation of 4.5 months. What length of warranty should be offered, if the
manufacturer wants to repair less than 1% of the televisions under the warranty?