ECO220Y5Y: Quantitative Methods in Economics
Test 3 – Topic 3
Time allowed 1 hour.
Answer all questions.
Calculators may be used.
No Outside Materials – Cheat Sheet included with test
Question 1
In the 2017 season Toronto FC (TFC) were a great team and Giovinco scored 25 goals in a stretch of 25
games. Based on the 2017 season answer the following: (assume Giovinco will play the first 25 games of
next season)
1. What is the probability he will score six or more goals in his first four games of the next season?
2. What is the probability he opens the first half of his first game in the next season with a brace (2
goals)?
3. Assume all games last exactly 90 minutes. What is the probability fans will have to wait 270 minutes
or longer into the first 25 games of next season until Giovinco scores his first goal?
4. Assuming Giovinco scores in a game then TFC win.
If he does not score they lose.
What is the
probability they will win at least 80% of the 25 games he plays next season?
Question 2
In each part assume the following and solve:
1. Assume
X
⇠
F
10
,
5
. Solve for
P
(
X
3
.
3).
2. Assume
X
⇠
F
1
,
23
. Solve for
P
(
X
6
.
25).
3. Assume
X
⇠
F
1
,
1
. Solve for
P
(
X
≥
1).
4. Assume
X
⇠
t
25
. Solve for
P
(

2
.
060
X

1
.
485).
page 1 of 2
ECO220Y
November 30, 2018
Question 3
Consider the following binomial distribution:
3.125
3.125
15.63
15.63
31.25
31.25
31.25
15.63
3.125
0
0
10
10
20
20
30
30
Percent
Percent
0
1
1
2
2
3
3
4
4
5
5
pdf
pdf
Binomial Density (PDF)
Binomial Density (PDF)
1. Solve for the mean and standard deviation of the binomial distribution
2. Solve for
P
(
X >
3) in the binomial distribution
3. Solve for the mean and standard deviation of ONE Bernoulli trial from this binomial distribution
4. Now assume there are 200 of these Bernoulli trials in the binomial.
Use an approximation to the
normal to solve for
P
(
X <
30) (use your p from part 3)
Question 4
Last summer the chance of failing ECO220 was 8%.
You decide to put together a random sample of 35
friends from ECO220 from the summer and use this to solve the following:
1. What is the mean and variance of the sampling distribution?
2. What is the probability that in your sample of friends between 2 and 4 of them failed?
(hint: use
sampling distribution)
3. What is the probability that in your sample more than 32 of them passed?
(hint:
use sampling
distribution)
page 2 of 2
Quantitative Methods in Economics
ECO220Y5Y – Cheat Sheet
Formulas & Statistical Tables for Economists
page 1 of 16