AQR – Fall 2014 Semester Review
Name____________________________ Period____
Due Wednesday, 12/17/14. Counts as two minor grades.
Use the following information to answer questions 1-2:
Actual mileage = k • odometer reading (mileage)
Actual speed = k • speedometer reading (miles per hour)
Where k =
circumference of bigger tire
circumference of factory-installed tire
1.
If the odometer reading is 8,000 miles on your car and you have tires with a circumference of 103 inches, you have
actually traveled ________ miles. (Factory-installed tires circumference is 93 inches.)
2.
If the speedometer reading is 40 mph on your car and you have tires with a circumference of 103 inches, you are
actually traveling ________ mph. (Factory-installed tires circumference is 93 inches.)
3.
The aspect ratio of tire P195/60R15 is
4.
You are standing amongst a crowd that is 5 feet deep and 2 miles long at a parade. You want to estimate how
many people are there. If each person occupies 2 square feet, estimate the size of the crowd watching the parade
along a 2 mile stretch. (Both sides of the street) (there are 5,280 feet in one mile)
5.
There are about 7,000,000,000 people living in the world. About how many males are there?
6.
How many phone numbers are possible in the (512) area code if:
.
For the form ABC-XXXX, A is restricted to 2-9 but X, B, and C can be any digit 0-9
Create a Venn Diagram to answer the questions for the following situations.
A marketing class polled 150 people at a shopping center to determine how many read the Daily News and how many read
the Weekly Gazette. They found the following:
95 just read the Daily News, 31 read both, 10 read neither.
7.
What is the probability that a person only reads the Weekly Gazette?
8.
P(reads both Daily News and Weekly Gazette)
9.
P(a person reads neither)
Use the following scenario to answer questions 10-12.
Kayla plays chess. Next week she will be competing in a tournament in which she will play 4 games. To win a trophy, she
must win at least 3 games.
10.
How many total possible outcomes can she have when she plays her 4 games?
11.
What is the probability she will win at least 2 games?
12.
What is the probability of winning a trophy?
Use the following scenario to answer questions 13-14.
Shari gets an allowance of $10 per week. She has decided she needs more money, so she has made a deal with her
mother in hopes of increasing her weekly allowance. She proposes that she will throw a dart at the dart board. If she hits the
board, she gets the original $10 plus another shot at the dartboard for an additional $10. If she misses the first throw, she
only gets $5 for the week. Shari hits the dart board 60% of the time.
13.
Shari's mom is worried about how often she will be giving her daughter $20 a week. Given Shari's stats, how many
weeks will her mom be out $20?
14.
How many weeks in a year will her mom only have to pay $10?
15.
Define compound probability (The “and” case):
You are eating lunch at Subway and have narrowed your sandwich choices to the items in the table below. You must
choose one item from each category and the estimated probability for each choice is included.
Bread
Honey Oat
(0.4)
Meat
Ham
(0.6)
Spread
Mayo
(0.5)
White
(0.6)
Turkey
(0.4)
Mustard
(0.2)
Ranch
(0.3)
Create a tree diagram showing all possible choices to help you answer questions 16-17.
16.
How many outcomes are there?
17.
P(honey oat, with ham and mayo or ranch)?
18.
Which of the following is part of an observational study?
a) Treatment
b) Placebo
c) Control group
d) Variable of interest
USE THE FOLLOWING TO ANSWER 19 – 24.
The dentists in a dental clinic would like to determine if there is a difference between the number of new cavities in people
who eat an apple a day and in people who don’t. They are going to conduct a study.
50 clinic patients who report that they routinely eat an apple a day and 50 clinic patients who report that they don’t will
be identified. The dentists will look at their records to determine the number of cavities the patients have had over the
past two years. They will then compare the number of new cavities in the patients.
19.
Is this study observational or experimental?
20. Who are the participants?
21.
What are the variables of interest?
22. Is there a treatment? If so, what is it?
23.
Is there a control group? Placebo?
24. Is there any sampling bias?
Use the following information for questions 25-28.
You are thrown 3 fastballs and you must hit them in a fair zone to count.
If you hit all 3 in a fair zone you win the big prize
If you hit 2 in a fair zone you win a medium size prize
If you hit 1 in the fair zone you get the small prize
If you hit zero you do not win and receive no prize.
25. What is the probability you will win the big prize?
26. What is the probability of getting nothing?
27. What is the probability of getting the small prize?
29.
Jar 1 has 6 marbles in it. Jar 2 has 4 cubes
in it. Find the probability of drawing out a red
marble and a red cube without looking.
28. What is the probability of winning a
medium prize?
Jar 1
Y
B
Jar 2
B
R
Y
R
R
B
G
Y
30.
You have decided to attend Florida State University, and are registering for classes. You are trying to get into one
of Professor Sumners’ Calculus sections. Here are the times Calculus is offered:
Prof. Sumners: Sec. 1: 8-9am; Sec. 2: 11-noon; Sec. 3: 2-3:20
Mr. Zhang:
Sec. 1: 9-10; Sec. 2: 10:15-11:15; Sec. 3: 3-5pm; Sec. 4: 8-noon
Prof. Yueng:
Sec. 1: 8-9:30am; Sec. 2: 10:15-11:45am; Sec. 3: 9-11am; Sec. 4: 2-4pm
Prof. Martinez: Sec. 1: 9:15-10am; Sec. 2: 2:30-3:15pm
If you only have room in your schedule for Morning classes (ending before noon) and you are assigned a morning
section at random, what are the odds you end up in Professor Sumners’ classes?
A. 22%
B. 33%
C. 15%
D. 25%
31.
You find out that all of Professor Sumners’ classes are full. You get assigned to another teacher’s class,
regardless of it being in the morning or afternoon, at random. What are the odds that you end up with a morning
class that will fit into your schedule?
32.
You toss a coin without looking at the board to the right of this question. Looking at the board as an area model,
what are the chances that your coin lands on a blue section?
33.
34.
35.
Mr. Price’s uses the following average for grading his Pre-Cal classes: Tests are 60% of the grade, quizzes count
30%, and homework is 10%. Mr. Price decides to offer his students a onetime chance to switch to a new grading
system or stay with the one listed above. The new grading system is: Tests are 50% of the grade, quizzes count
35%, and homework is 15%. Elvis has a quiz average of 76 and a homework average of 90 and a test average of
87. What would his average be under each of the systems?
Another one of Mr. Price’s students Chris is trying to decide if he should stay with the old system or change to the
new one. He has a quiz average of 74, homework of 80, and a test average of 76. What would his average be
under each of the systems?
It is Joe Blow’s first season of playing baseball with the Marlins. He has had 280 at-bats resulting in 51 singles, 12
doubles, 29 triples, and 7 homeruns. How many more triples, doubles, singles, and homeruns would Joe need to
have a .817 slugging average? Round to 3 decimal places.
a) 1 single, 2 doubles, 3 triples, 4 homeruns
b) 4 singles, 6 doubles, 1 triple, 5 homeruns
c) The correct answer is not here.
Use the following data to answer the following questions 39-40: 20 33 32 75 25 36 25 24 33 26
36.
What is the mean of the data?
37.
What is the median of the data?
38.
What is the range of the data?
41.

Define the following and give an example of each:

placebo effect

control group

treatment
variable of interest
For # 42 -44, determine the following:
 Observation or experimental
 Variable(s) of interest
 Treatments
 Experimental units/participants
42.
A clinical trial is set up to compare a proposed new drug with a placebo (some inert substance that is given to make
people think they are talking a drug when they are not). 50 patients are recruited, and we randomly select 25 of
them to receive the new drug, the rest receiving the placebo. After some period of time the two groups are
compared to see whether the group receiving the new drug has recovered from the disease under study.
43.
In an attempt to study the health effects of air pollution, a group of researchers selected 6 cities in very different
environments some from an urban setting (e.g. greater Boston), some from a heavy industrial setting (e.g. eastern
Ohio), some from a rural setting (e.g. Wisconsin). Altogether they selected 8000 subjects from the 6 cities, and
followed their health for the next 20 years. At this time their health prognoses were compared with measurements of
air pollution in the 6 cities.
44. A study in California showed that students who study a musical instrument have higher GPAs than students who do not,
3.59to 2.91. Of the music students, 16% had all As, compared with only 5% among the students who did not study a
musical instrument.
45. Consider the graph:
A
B
E
F
D
C
a.
How many edges are in the graph?
b.
How many vertices are adjacent to D?
c.
Does the graph have an Euler Circuit?
d.
Why or why not?
e.
Does the graph have an Euler path?
f.
If it has an Euler path, identify the path
H
46. Use Kruskal’s algorithm to find the minimally spanning tree.
G