BUSS1020 Study Guide - Final Guide: Yougov, The Wall Street Journal, Covariance

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Published on 4 Aug 2020
Department
Course
Professor
BUSS1020 Workshop 5 Solutions
Learning the Basics
Question 1
Given the following probability distributions:
Distribution A
Distribution B
xi
P(X = xi)
xi
P(X = xi)
0
0.5
0
0.05
1
0.2
1
0.1
2
0.15
2
0.15
3
0.1
3
0.2
4
0.05
4
0.5
a. Compute the expected value for each distribution.
b. Compute the standard deviation for each distribution.
c. Compare the results of distributions A and B.
(Use Excel and hand calculation (calculator) to check, Also confirm that each is a probability
distribution (i.e. the probabilities add to 1).
Question 2
The manager of the commercial mortgage department of a large bank has collected data during the
past two years concerning the number of commercial mortgages approved per week. The results
from these two years (104 weeks) are as follows:
Number of Commercial
Mortgages Approved
Frequency
0
13
1
25
2
32
3
17
4
9
5
6
6
1
7
1
a. Compute the expected number of mortgages approved per week.
b. Compute the standard deviation.
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Question 3
Determine which of the following are, or are not, valid probability distributions, and then explain
why or why not. Calculate the expectation for each actual distribution.
A
B
C
X
P(X)
Y
P(Y)
Z
P(Z)
1
0.2
0
-0.1
-2
0.1
2
0.2
2
0.2
-1
0.1
3
0.3
4
0.3
1
0.1
4
0.4
5
0.4
2
0.7
Question 4
Assuming the random variable follows the Hypergeometric distribution, determine the following:
a. If n = 4, N = 10, and E = 5, find P(X = 3).
b. If n = 4, N = 6, and E = 3, find P(X = 1).
c. If n = 5, N = 12, and E = 3, find P(X = 0).
d. If n = 3, N = 10, and E = 3, find P(X = 3).
Applying the Techniques.
Question 5
A lock on a bank vault consists of three dials, each with 30 positions. In order for the vault to open,
each of the three dials must be in the correct position.
a. How many different possible dial combinations are there for this lock?
Repetition: 
b. What is the probability that if you randomly select a position on each dial, you will be able
to open the bank vault?
 

  
Question 6
A team is being formed that includes four different people. There are four different positions on
the teams. How many different ways are there to assign the four people to the four positions?
Permutation:
 
Question 7
There are eight members of a team. How many ways are there to select a team leader, assistant
team leader, and team coordinator?
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Permutation:
 
Question 8
BUSS 1020 consisted of 1200 Commerce students in 2011. These students were asked, “To the
nearest hour, how many hours did you study statistics last week?” The lecturer was only interested
in the responses of the students in that one class, so the 1200 students constitute a population. The
probability distribution of the responses is shown in the following table:
X = hours of
study
Number of
students
Probability
0
96
96/1200=0.08
1
168
168/1200=0.14
2
300
300/1200=0.25
3
216
216/1200=0.18
4
156
156/1200=0.13
5
132
132/1200=0.11
6
84
84/1200=0.07
7
36
36/1200=0.03
8
12
12/1200=0.01
Total
1200
1
Using Excel, calculate:
a. What is the mean number of hours studied the previous week in this population?
 
b. What is the standard deviation of the number of hours studied in the previous week?
 
c. Verify that Chebyshev’s rule works for this distribution when k=2, 3.
Question 9
According to a survey, 95% of the subscribers to The Wall Street Journal Interactive Edition have
a computer at home. For those households, the probability distributions for the number of laptop
and desktop computers are given in the table below. (The Wall Street Journal Interactive Edition
Subscriber Study, 1999)
Number of
computers
Laptop
Desktop
0
0.47
0.06
1
0.45
0.56
2
0.06
0.28
3
0.02
0.1
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