Name: 

Determine the range 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

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

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

Lightning Strikes (per square kilometre)	Frequency
0.00–0.19	13
0.20–0.39	2
0.40–0.59	6
0.60–0.79
0.80–0.99	3
1.00–1.19	1

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.

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 standard deviation, 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.

Which set is normally distributed?

Interval	0–9	10–19	20–29	30–39	40–49	50–59
Set A.	100	500	850	820	450	150
Set B.	800	750	700	650	600	550
Set C.	950	420	180	220	460	990
Set D.	400	620	760	820	900	850

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

The results of a survey have a confidence interval of 28% to 34%, 19 times out of 20.
Determine the margin of error.

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

What system of linear inequalities is shown here?

What system of linear inequalities is shown here?

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}

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.
How would you write the objective function for revenue, R?

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

Constraints:
y 0
x y + 10
2x + y 80

Objective function:
T = 2y – x

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?

Environment Canada compiled data on the number of lightning strikes per square kilometre in Quebec towns from 1999 to 2008.
1.41      0.96      0.48      0.30      0.03
1.32      0.90      0.47      0.19      0.02
1.25      0.71      0.29      0.18      0.02
1.11      0.57      0.49      0.15      0.00
1.02      0.41      0.10      0.11     
1.01      0.17      0.49      0.08     
0.98      0.99      0.32      0.04     

Determine the standard deviation, to two decimal places.

The ages of members in a hiking club are normally distributed, with a mean of 32 and a standard deviation of 6 years. What percent of the members are between 26 and 32?

Determine the percent of data to the right of the z-score: z = 1.60.

Is the point (–2, 2) in the solution set for the linear inequality 10y – 12x > 5?

A system of linear inequalities has vertices at (2, 4), (–2, 5), and (0, 0).
Which point represent the maximum value of the objective function Z = 4y + x?

a) Use confidence intervals to interpret the following statement and apply the result to a graduating class of 1400 students.
In a recent survey, 72% of post-secondary graduates indicated that they expected to earn at least $6000/month by the time they were ready to retire. The survey is considered accurate within ±5.2%, 19 times in 20.
b) How could they increase the confidence level of their result?

An advertisement for a new toothpaste states that 80% of users reported better dental check-ups. The results of the poll are accurate within 4 percent points, 9 times out of 10.
a) State the confidence level.
b) Determine the confidence interval.
c) In a focus group of 50 students, four said they already used this toothpaste and another five did not want to try it. Determine the range of the mean number of the remaining students who could expect better dental check-ups.

Two different market research companies conducted a survey on the same issue. Company A used a 90% confidence level and company B used a 95% confidence level.
a) If both companies used the same sample size, what does this imply about the margin of error for each survey?
b) If both companies used the same margin of error of ±3.5%, what does this imply about the sample size for each survey?

Four teams are travelling to a lacrosse tournament in cars and minivans.
• Each team has no more than 2 coaches and 13 athletes.
• Each car can take 4 team members, and each minivan can take 7 team members.
• No more than 5 minivans and 8 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
4c + 7m 60
c 8
m 5
Objective function to maximize:
V = c + m

The stylists in a hair salon cut hair for women and men.
• The salon books at least 3 women’s appointments for every man’s appointment.
• Usually there are 120 or more appointments, in total, during a week.
• The salon is trying to reduce the number of hours the stylists work.
• A woman’s cut takes about 60 min, and a man’s cut takes about 25 min.
What combination of women’s and men’s appointments would minimize the number of hours the stylists work? How many hours would this be?