Name: 

Determine the mean of the following test scores.
History Test 2 Scores (out of 100)
95      85      72      62
92      84      72      59
89      80      70      52
88      78      68      40
85      73      67      32

A pear orchard has 40 trees with these heights, given in inches.
      110      105      83      84      104      92      95      98
      88      92      80      81      115      88      106      92
      97      103      100      93      98      93      93      102
      92      87      117      92      75      102      83      107
      122      92      115      86      89      98      105      125

What value goes in the second row of this frequency table?

Height (in.)	Frequency
70–79	1
80–89
90–99	14
100–109	9
110–119	4
120–129	2

A company measured the lifespan of a random sample of 30 light bulbs. Times are in hours.
      985      1001      1024      1087      952
      910      938      931      1074      1081
      1078      1080      982      1108      1022
      937      922      1017      1093      1115
      880      1048      917      1086      935
      936      986      1038      954      966

What value goes in the fourth row of this frequency table?

Lifespan (hours)	Frequency
850–899	1
900–949	8
950–999	6
1000–1049
1050–1099	7
1100–1149	2

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?

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 older than 60?

Determine the z-score for the given value.
µ = 184, s = 8.6, x = 174

Determine the percent of data to the right of the z-score: z = –0.08.

Determine the percent of data between the following z-scores:
z = 0.40 and z = 1.80.

A poll was conducted about an upcoming election. The result that 30% of people intend to vote for one of the candidates is considered accurate within ±4.5 percent points, 19 times out of 20.
State the confidence interval.

Which sample size will have the least margin of error?

For which inequality is (5, 0) a possible solution?

Which test point is in the solution set for the linear inequality
{(x, y) | 7x + 5y 0, x I, y I}?

Identify the point of intersection for the following system of linear inequalities.
{y – 3x < 12, x + y 0, x R, y R}

Identify the point of intersection for the following system of linear inequalities.
{y 2 + x, x + y 0, x R, y R}

Describe the boundary lines for the following system of linear inequalities.
{2y – 6x < 12, 4x + 4y 8, x   I, y   I}

Which point in the model below would result in the maximum value of the objective function W = 5y – 10x?

The following model represents an optimization problem. Determine the maximum solution.
Restrictions:
x R
y R

Constraints:
x 4
x – y 12
x + 3y 24

Objective function:
G = x – 2y

Brent found spiders and grasshoppers in his barn.
• There were at most 15 spiders and at most 20 grasshoppers.
• There were no more than 30 spiders and grasshoppers, in total.
Let s represent the number of spiders and let g represent the number of grasshoppers.
Which inequality represents a restriction of s and g based on the given information?

Brent found spiders and grasshoppers in his barn.
• There were at most 15 spiders and at most 20 grasshoppers.
• There were no more than 30 spiders and grasshoppers, in total.
• All the spiders had eight legs and all the grasshoppers had six legs.
What is the maximum number of legs on all the spiders and grasshoppers in his barn?

Audrey notices the number of people and dogs in a dog park.
• There are more people than dogs.
• There are at least 12 dogs.
• There are no more than 40 people and dogs, in total.
Let d represent the number of dogs and let p represent the number of people.
Which inequality represents a restriction of d and p based on the given information?

Joel researched the average daily temperature in his town.
Average Daily Temperature in Lloydminster, SK

Month

Jan.

Feb.

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

average daily temperature (°C)

–10.0

–17.5

–5.0

3.7

10.7

14.3

20.1

14.0

9.8

4.8

–5.8

–14.8

Determine the mean of the data to the nearest tenth of a degree.

Environment Canada compiled data on the number of lightning strikes per square kilometre in Saskatchewan and Manitoba towns from 1999 to 2008.
2.03      1.31      0.25      1.03      1.20      0.17
0.99      1.01      0.24      0.94      0.92      0.09
0.86      0.71      0.05      0.81      0.63      0.01
0.80      0.58      0.00      0.72      0.49      0.52
0.43      0.46      0.40

If the interval width is 0.5 and starts at 0.00, which range of data has no entries?

Four groups of students recorded their pulse rates after a 2 km run.

Group 1	126	168	158	192	146	166	104	164	116	138	172	136	152	128
Group 2	158	132	156	160	108	150	178	136	172	140	126	154	130	160
Group 3	136	174	156	176	150	166	142	156	130	182	180	166	148	172
Group 4	144	150	142	152	174	176	118	152	178	164	128	158	158	166

Determine the mean of Group 1, to one decimal place.

A poll was conducted about an upcoming election. The result that 65% of people intend to vote for one of the candidates is considered accurate within ±4.2 percent points, 9 times out of 10.
State the confidence interval.

Is the point (0, 0) in the solution set for the following system of linear inequalities?
{7y – 2x 5, y > 3x – 5, x I, y I}

The manager of a customer support line currently has 250 unionized employees. Their contract states that the mean number of calls that an employee should handle per day is 45, with a maximum standard deviation of 7 calls. The manager tracked the number of calls that each employee handles. Does the manager need to hire more employees if the calls continue in this pattern?

Daily Calls	Frequency
26–30	3
31–35	15
36–40	44
41–45	76
46–50	63
51–55	39
56–60	8
61–65	2

For every quilt that is sold at a fundraising banquet, $90 goes to charity. For every ticket that is sold, $65 goes to charity. The organizers’ goal is to raise at least $7000. The organizers need to know how many quilts and tickets must be sold to meet their goal.
a) Define the variables and write a linear inequality to represent the situation.
b) Graph the linear inequality to help you determine whether each of the following points is in the solution set. The first coordinate is the number of quilts and the second is the number of tickets.
i) (40, 50)      ii) (10, 100)      iii) (20, 75)

A banner is being created for a soccer team.
• The length must be less than 250 cm.
• The perimeter must be 600 cm or less.
Use a graph to choose three possible combinations of length and width. Explain your choices.

A student council is ordering signs for the autumn dance. Signs can be made in letter size or poster size.
• No more than 50 of each size are wanted.
• They need at least 20 poster size signs.
• No more than 75 signs are needed altogether.
• Letter-size signs cost $6.50 each, and poster-size signs cost $10.95 each.
The student council wants to minimize the cost of printing.
a) Create a model to represent this situation.
b) Suppose that there is an additional $15 fee to set up the printers. How would your model change?

A refinery produces oil and gas.
• At least 1.5 L of gasoline are produced for each litre of heating oil.
• The refinery can produce up to 8.5 million litres of heating oil and 4 million litres of gasoline each day.
• Gasoline is projected to sell for $1.05 per litre. Heating oil is projected to sell for $1.90 per litre.
The company needs to determine the daily combination of gas and heating oil that must be produced to maximize revenue. Create a model to determine this combination. What would the revenue be?
Optimization Model
Let g represent the number of millions of litres of gasoline.
Let h represent the number of millions of litres of heating oil.
Let R represent the total revenue from sales in millions of dollars.
Restrictions:
g Î R, h Î R
Constraints:
g 0
h 0
g 1.5h
g 4
h 8.5
Objective function to maximize:
R = 1.05g + 1.90h