ECON1005 Mid Semester # 2 Review Packet
The following concepts can be tested on Mid Semester #2. Use the following check list and the review problems to
help you in your studying.
This packet is not meant to be a comprehensive review packet, but it is to be used along with your class notes, problem
sets and chapter readings. This packet is created to assist you in your review. It only illustrates the types of questions
that may come on the exam. The answer key is provided in a separate file. It is for review only and is no reflection
of the number of questions that will be on the exam. Irrespectively of the number of questions, the mid semester exam
can be completed in an hour or less.
Note that although the test is limited to the topics listed in the table below, there are a myriad of ways to present such
questions (whether long answer or multiple choice). Again, you are strongly encouraged to practice the questions
completed in lectures and all the questions on the tutorial sheets (tutorial questions + extra questions).
The z table can be found at the end of this packet.
Concept
Basic probability (including definitions, axioms and calculations)
Types of events (including independent, mutually exclusive, exhaustive, etc.)
Calculating probabilities from two-way tables (marginal, conditional, joint)
General discrete probability distributions (including how to use them (tables, functions, raw
information), calculation of probabilities, expected values, variances)
Binomial probability distributions (distribution function, calculation of probabilities, mean,
variance, etc.)
Normal probability distributions (including properties, standardization - z-scores, probabilities,
using tables, forward problems, backward problems)
Normal approximation to the binomial distribution
Reviewed
ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
1. If two events (both with probability greater than 0) are mutually exclusive, then:
a)
b)
c)
d)
e)
They also must be independent.
They also could be independent.
They also must be complements.
They also could be complements.
They cannot be complements.
2. A box of 8 marbles has 4 red, 2 green and 2 blue marbles. If you select one marble, what is the probability that
it is a red or blue marble.
a)
b)
c)
d)
0.60
0.75
6.00
0.80
3. Suppose that the probability of event A is 0.2 and the probability of event B is 0.4. Also, suppose that the two
events are independent. Then P(A|B) is:
a)
b)
c)
d)
P(A) = 0.2
P(A)/P(B) = 0.2/0.4 = 0.5
P(A) × P(B) = (0.2)(0.4) = 0.08
None of the above
4. A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming the
results are independent for the two patients, what is the probability that neither one of them will be successfully
cured?
a)
b)
c)
d)
0.5
0.36
0.2
0.04
5. Workplace accidents are categorized in three groups: minor, moderate and severe. The probability that a given
accident is minor is 0.5, that it is moderate is 0.4, and that it is severe is 0.1. Two accidents occur independently
in one month. Calculate the probability that neither accident is severe and at most one is moderate.
a)
b)
c)
d)
e)
0.25
0.40
0.45
0.56
0.65
2
ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
6. Thirty percent of the managers in a certain company have MBA degrees as well as professional training.
Eighty percent of all managers in the firm have professional training. If a manager is randomly chosen and
found to have professional training, what is the probability that he/she also has an MBA?
a)
b)
c)
d)
e)
0.240
0.260
0.375
0.500
0.625
USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 7 & 8: A random sample of 80
lawyers was asked if they were in favour of the Caribbean Court of Justice (CCJ) or against it. The results are
given in the table below.
Favours CCJ
Against CCJ
Male
32
24
Female
13
11
7. If a lawyer is randomly selected from this group, the probability that the lawyers is against the CCJ or is a male
is
a)
b)
c)
d)
e)
24/80
35/80
45/80
56/80
67/80
8. If a lawyer is randomly selected from this group, the probability that this lawyer is against the CCJ given that
the lawyer is a female is
a)
b)
c)
d)
e)
11/80
13/45
24/80
11/35
11/24
3
ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 9 to 11: The following table are the
results from a random sample of 173 drivers registered with ICUI insurance company.
Age
Number of Accidents in a Year
0
1
2
17 – 25
18
14
10
26 – 45
38
12
8
Over 45
52
10
11
9. The probability of a selected driver having 2 accidents in a year is a/an
a)
b)
c)
d)
e)
conditional probability
independent probability
joint probability
marginal probability
mutually exclusive probability
10. The probability of an over 45 driver having 1 accident in a year is a/an
a)
b)
c)
d)
e)
conditional probability
independent probability
joint probability
marginal probability
mutually exclusive probability
11. The probability of a selected driver being under 26 and having no accidents in a year is a/an
a)
b)
c)
d)
e)
conditional probability
independent probability
joint probability
marginal probability
mutually exclusive probability
12. If A and B are two events such that P(A) = 0.5, P(B) = 0.1 and P(A ∩ B) = 0.3. Which of the following is true?
a)
b)
c)
d)
e)
A and B are independent and mutually exclusive.
A and B are mutually exclusive.
A and B are dependent.
A and B are independent.
A and B are conditional events.
4
ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
1
13. Let E and F be two independent events. If the probability that both E and F happen is 12 and the probability
1
that neither E nor F happens is 2, then P(E) and P(F) respectively are:
a)
1
3
,
1
4
b)
1
2
,
1
6
c)
1
12
, 1
d)
2
3
,
1
4
e)
1
2
,
2
6
14. Suppose we have a loaded die which has the following probability distribution.
The expected value of this die is
a)
b)
c)
d)
3.00
3.25
3.30
4.50
15. The payoff (X) for a lottery game has the following probability distribution.
Payoff
$0
$5
Probability
0.8
0.5
If you play the game, what is your expected payoff?
a)
b)
c)
d)
$0
$0.50
$1.00
$2.50
5
ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
16. If the random variable X is defined as the number of cars at a traffic light in Half-Way-Tree at 5am on a given
day, the P(X > 5) is equal to
a) P(X > 5) = P(X ≥ 5)
b) P(X > 5) = P(X ≥ 6)
c) P(X > 5) = 1 – P(X < 5)
d) P(X > 5) = 1 – P(X ≤ 6)
e) P(X > 5) = 1 – P(X ≤ 4)
USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 17 & 18: A random variable X has
the following probability distribution.
X
-1
0
2
4
P(X = x)
0.2
0.3
0.3
0.2
17. The expected value of X is
a)
b)
c)
d)
e)
0.30
1.20
1.60
1.67
5.00
18. The variance of X is
a)
b)
c)
d)
e)
1.20
1.60
2.14
3.16
4.60
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ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 19 to 22: The number of patients
waiting to see a doctor in a given hour has the following probability distribution function.
𝑓(𝑥) =
2𝑥−1
16
for x = 1, 2, 3, 4
19. What is the probability that more than one patient is waiting to see the doctor in a given hour?
a) 0/16
b) 1/16
c) 4/16
d) 12/16
e) 15/16
20. What is the probability that there are no patients waiting to see the doctor in a given hour?
a) 0/16
b) 1/16
c) 4/16
d) 12/16
e) 15/16
21. The average number of patients waiting to see the doctor in a given hour is
a)
b)
c)
d)
e)
1.00
2.50
3.13
9.18
40.00
22. The variance of the number of patients waiting to see the doctor in a given hour is
a)
b)
c)
d)
e)
0.859
3.125
7.500
9.766
10.625
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ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
23. Which one of these variables is a binomial random variable?
a)
b)
c)
d)
Time it takes a randomly selected student to complete a multiple-choice exam
Number of textbooks a randomly selected student bought this term
Number of women taller than 68 inches in a random sample of 5 women
Number of CDs a randomly selected person owns
24. Let X be a binomial random variable with n = 25 and p = 0.6. The probability that more than 12 successes will
occur is
a)
b)
c)
d)
0.0808
0.1539
0.8461
0.9191
25. Abigail takes three standardized tests. She scores 600 on all three. Rank her relative performance on the three
tests from best to worst if the means and standard deviations for the tests are as follows:
a)
b)
c)
d)
e)
Mean
Standard Deviation
Test I
500
80
Test II
470
120
Test III
560
30
I, II, and III
III, II, and I
I, III, and II
III, I, and II
II, I, and III
26. The distribution of enrolment in a class is normal with a mean if 55 and a standard deviation of 5. If a
particular observation has a standard score of -1, it can be concluded that:
a)
b)
c)
d)
The value of the observation is 60
The value of the observation is between 55 and 60
The value of the observation is 50
The value of the observation is greater than 55
8
ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
27. A researcher interested in the age at which women are having their first child surveyed a simple random sample
of 250 women having at least one child and found an approximately normal distribution with a mean age of
27.3 and a standard deviation of 5.4. Approximately 95% of the women had their first child between the ages
of
a)
b)
c)
d)
e)
11.1 years and 43.5 years
16.5 years and 38.1 years
21.9 years and 32.7 years
21.9 years and 38.1 years
25.0 years and 29.6 years
28. A bag contains 7 red marbles and 5 white ones. Three marbles are drawn without replacement (one after the
other). Let X be the number of red marbles in the sample. Which of the following statement is NOT true?
a)
b)
c)
d)
e)
X is a discrete random variable.
The possible values of X are 0, 1, 2 and 3.
X is a binomial random variable.
The probability of getting a red marble on the first draw is 7/12.
The probability of getting a red marble on the second or third draw is dependent on what was drawn
before.
29. Let X be the time it takes a company’s technician to install a phone line in a private home. X ~ N(20, 5). What
is the probability that it will require more than 25 minutes for the technician to install the phone line?
a)
b)
c)
d)
e)
0.1587
0.3174
0.3413
0.6826
0.8413
30. Tina's score on her midterm exam was at the 50th percentile. The grades were normally distributed. The exam
average was 78 and the standard deviation was 6. What was Tina's score on the exam?
a)
b)
c)
d)
90
84
50
78
31. Marsha recently had a baby. She named him Mark. Marsha was told that the weights of babies born in this
hospital are normally distributed and the mean is 7.5 lbs, with a standard deviation of 0.25 lbs. Mark’s weight
at birth was in the 15th percentile. How much did Mark weigh when he was born?
a)
b)
c)
d)
7.240 lbs
7.500 lbs
7.625 lbs
7.750 lbs
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ECON1005: Introductory Statistics
Mid Semester #2 Review Packet vs2
32. Carlton has a z-score of 1.74 on the achievement test. Did he score higher than my score in the 98th percentile?
What was Carlton's score?
a)
b)
c)
d)
Carlton scored higher than I. His score was 3288.
Carlton scored higher than I. His score was 1461.
Carlton scored lower than I. His score was 261.
Carlton scored lower than I. His score was 1461.
33. The school wants to allow all students with scores in the top 3% into a special advanced programme. What will
be the minimum score required to be admitted into this programme?
a)
b)
c)
d)
e)
31.20
50.01
50.99
56.18
68.80
34. The records of an Italian shoe manufacturer show that 10% of shoes made are defective. Assuming
independence, find the probability of getting:
a) 2 defective shoes in a batch of 12.
b) 6 defective shoes in a batch of 20.
35. The owner of a small restaurant is trying to quantify the variation in the daily demand for takeout lunches. She
has decided to assume that the demand is normally distributed. She knows on average 100 takeout lunches are
purchased daily and that 90% of the time, the daily demand is below 116.
a) What is the standard deviation of this distribution?
b) The owner of the restaurant wants to stock enough boxes each day so that the probability of running out
of boxes is no higher than 0.05. What is the lowest number of boxes she should stock to achieve this?
36. A restaurant provides lunches for office workers in New Kingston. From past data, it was estimated that the
probability that an office worker orders curry goat is one-third. If on a given day there are 90 orders for
lunches and the chef prepares 40 curry goat lunches, what is the probability that there will be more request for
curry goat lunches than can be met?
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