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

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Published on 4 Aug 2020

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Department

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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.

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?

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