Name: 

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?

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 pear orchard has 20 trees with these heights, given in inches.
      110      83      104      95
      88      80      115      106
      97      100      98      93
      92      117      75      83
      122      115      89      105

Determine the mean, to one decimal place.

Environment Canada recorded the amount of rain (in millimetres) in Victoria, BC for two months.
0      0      9.0      0      0      1.0      0
0      0      7.6      0      0      5.8      0.6
0      0      0.4      0      0      0
0      0      0      0      0      0
0      0      0      0      0      0
0      0      0      0      0      0.4
0      5.8      0      0      1.6      0.2
0      6.0      0      0      0.2      0
0      0.2      0      0      1.0      0
0      2.8      0      0      26.0      0

Determine the standard deviation, to one decimal place.

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

Determine the standard deviation, to two decimal places.

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 30 and 50?

Determine the percent of data to the left of the z-score: z = –1.50.

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 = –2.25 and z = 1.75.

The results of a survey have a confidence interval of 56.0% to 64.6%, 9 times out of 10.
Determine the margin of error.

The results of a survey have a confidence interval of 4.8% to 7.2%, 19 times out of 20.
Determine the margin of error.

Which test point is in the solution set for the linear inequality
{(x, y) | 5x – 2y 10, x R, y R}?

How would you graph the solution set for the linear inequality 2y – 2x 10?

Identify the point of intersection for the following system of linear inequalities.
{2y – 6x < 12, 4x + 4y 8, x   I, y   I}

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

Which test point is in the solution set for the following system of linear inequalities?
{2x – 5y < 2, x + y < 0, x   R, y   R}

What system of linear inequalities is shown here?

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.
What are the restrictions on x and y?

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

Constraints:
0 x 100
–50   y 50
x 25 – y
x – y 60

Objective function:
A = y – 2x + 10

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.
• All the dogs have four legs and all the people have two legs.
What is the maximum number of legs at the park?

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 0.25 and starts at 0.00, how many intervals are there?

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 standard deviation of Group 2, to one decimal place.

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 standard deviation of Group 4, to one decimal place.

A poll was conducted about an upcoming election. The results are considered accurate within ±4.0 percent points, 9 times out of 10.
State the confidence level.

Baskets of fruit are being prepared to sell.
• Each basket contains at least 8 apples and more than 4 oranges.
• Apples cost 25¢ each, and oranges cost 40¢ each.
• The budget allows no more than $6, in total, for the fruit in each basket.
Let x represent the number of apples.
Let y represent the number of oranges.
Write a linear inequality to represent the cost of each basket (in dollars).

A manufacturer collects data on the lifespan of their irons, in years.
4.0      2.8      6.8      7.0      6.8      5.8      5.0      6.0      4.2      5.4
7.0      4.8      7.4      5.0      6.0      7.8      4.6      5.2      6.4      5.0
5.4      5.8      6.2      6.2      5.6      6.4      6.4      6.6      4.8      5.8
5.8      5.4      5.2      5.6      6.2      4.4      6.4      5.6      6.0      6.2
5.2      5.8      7.6      4.6      5.6      5.6      6.4      6.0      6.4      4.8
4.4      3.2      7.2      7.4      7.2      6.2      5.4      6.4      4.6      5.8
7.4      5.2      7.8      5.4      6.4      8.2      5.0      5.6      6.8      5.4
a) Determine the mean and the standard deviation.
b) Draw a frequency polygon to show the data.
c) Does the data have a normal distribution? Explain.

The mass of an adult female Kodiak bear is generally in the range of 500 kg to 700 kg with a standard deviation of 50 kg. Male Kodiak bears typical weigh about 40% more than the females. Assuming that the data is normally distributed, determine the mean and standard deviation for the mass of an adult male Kodiak bear. Justify your answers.

Indy volunteers to fold origami cranes and swans for a display.
• She has 20 squares of white paper for the cranes and swans.
• It takes her 5 min to fold an origami crane and 4 min to fold an origami swan.
• There must be at least two swans for every crane.
• Indy needs a 10 minute break halfway through the job.
She wants to minimize the time spent doing origami.
a) Create a model to represent this situation.
b) Suppose that Indy’s given another 5 squares of origami paper. How would your model change?

Three teams are travelling to a hockey tournament in cars and minivans.
• Each team has no more than 2 coaches and 18 athletes.
• Each car can take 3 team members, and each minivan can take 5 team members.
• No more than 7 minivans and 15 cars are available. The school wants to know the combination of cars and minivans that will require the maximum number of vehicles. Create and verify a model to represent this situation.
a) Use the optimization model to determine the combination of cars and minivans that will use the maximum number of vehicles.
b) How many team members can travel in the maximum number of vehicles?
Optimization Model
Let V represent the total number of vehicles.
Let c represent the number of cars.
Let m represent the number of minivans.
Restrictions:
c Î W, m Î W
Constraints:
c 0
m   0
3c + 5m 60
c 15
m 7
Objective function to maximize:
V = c + m

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