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BUSINESS STATISTICS
MULTIPLE CHOICE TEST
SPRING 2003
SUBJECT CODE:
QBM117
DATE:
8 October 2003
TIME ALLOWED:
90 minutes only
CLOSED/OPEN BOOK:
Open book.
VALUE:
10% of the total assessment
INSTRUCTIONS
1.
2.
3.
4.
5.
6.
7.
Enter your name and student number in the space provided on the answer
sheet as directed by the lecturer. Use a 2B pencil only.
Answer all 20 questions, each question has equal value. Marks are not
deducted for incorrect responses.
Each question has five responses A to E. On the answer sheet colour the
response that best answers the question. If your answer differs from all
responses provided, select that response that best approximates your answer.
Make heavy marks that fill the circle completely.
Erase cleanly any answers you may wish to change.
When you have completed the exam, hand in the answer sheet only.
Calculators are permitted
QBM117 Multiple Choice Test – Spring 2003
Page 1 of 10
1.
An office supply catalogue gives a description of bookshelves that includes the
following variables. Which of these variables is qualitative?
A.
B.
C.
D.
E.
The width of a bookshelf.
The price of a bookshelf.
The height of a bookshelf.
The colour of a bookshelf.
The depth of a bookshelf.
Use the information following to answer questions 2. and 3.
A sample was taken of the salaries of 14 randomly selected employees of a large
company. The following are the salaries (in thousands of dollars) for this year.
60
2.
35
37
61
32
49
67
54
42
53
42
The mean = 49.7 and the standard deviation = 12.2
The range = 43 and the mean = 49.7
The mean = 48 and the mode = 42
The range = 43 and the standard deviation = 12.2
There is no mode and the standard deviation = 12.6
7
17
25
17.5
18
When analysing quantitative data, the following graphical device is not
appropriate:
A.
B.
C.
D.
E.
5.
75
The interquartile range for the salaries (in thousands of dollars) for this year is
A.
B.
C.
D.
E.
4.
47
Which of the following statements about the descriptive statistics (given in
thousands of dollars) for these data are correct?
A.
B.
C.
D.
E.
3.
42
Stem and leaf display
Histogram
Boxplot
Pie chart
Ogive
If the mean of a distribution is 5, the median is 6 and the mode is 7, then the
distribution is:
A.
B.
C.
D.
E.
negatively skewed.
symmetric.
bimodal.
positively skewed.
uniform.
QBM117 Multiple Choice Test – Spring 2003
Page 2 of 10
6.
The following marks are obtained by 5 students on a test:
8
16
24
4
13
The lecturer calculates the median to be 13. The lecturer however, then
discovers that an error was made when recording the marks. The mark of 24 is
actually a mark of 17. The new median would be:
A.
B.
C.
D.
E.
6
13
17
10.5
None of the above.
Use the information following to answer questions 7. and 8.
A sample of 400 university academics was taken. Each academic was asked their age,
sex, rank, annual salary, faculty and how many years they have been an academic.
The following pie chart provides information about the ranks of the 400 academics
sampled.
Pie Chart of the Rank of a Sample of 400 University Academics
Senior Lecturer
32%
Associate Professor
41%
Professor
14%
7.
Lecturer
13%
Based on the pie chart above, we may conclude that
A.
B.
C.
D.
E.
Associate Professors have the highest annual incomes.
less than half of the academics sampled are Professors or Associate
Professors.
Lecturers have the lowest annual incomes.
less than a quarter of the academics sampled are Professors.
Senior Lecturers earn more than Lecturers.
QBM117 Multiple Choice Test – Spring 2003
Page 3 of 10
8.
Which of the following bar graphs presents the same information as the pie
chart?
A.
Bar Chart of the Rank of a Sample of 400
Academics
Number of
Academics
200
150
100
50
0
Associate
Professor
Lecturer
Professor
Senior
Lecturer
Rank of Academic
B.
Bar Chart of the Rank of a Sample of 400
Academics
Number of
Academics
200
150
100
50
0
Associate
Professor
Lecturer
Professor
Senior
Lecturer
Rank of Academic
C.
Bar Chart of the Rank of a Sample of 400
Academics
Number of
Academics
200
150
100
50
0
Associate
Professor
Lecturer
Professor
Senior
Lecturer
Rank of Academic
QBM117 Multiple Choice Test – Spring 2003
Page 4 of 10
D.
Number of
Academics
Bar Chart of the Rank of a Sample of 400
Academics
160
140
120
100
80
60
40
20
0
Associate
Professor
Lecturer
Professor
Senior
Lecturer
Rank of Academic
E.
Bar Chart of the Rank of a Sample of 400
Academics
Number of
Academics
200
150
100
50
0
Associate
Professor
Lecturer
Professor
Senior
Lecturer
Rank of Academic
9.
The management of Disney world is interested in the time that people have to
wait for a monorail. The following boxplot shows the distribution of the
waiting times.
Box Plot of the Waiting Times for a Monorail at Disney World
4.5
6.5
8.5
10.5
12.5
14.5
16.5
18.5
Waiting Time (minutes)
QBM117 Multiple Choice Test – Spring 2003
Page 5 of 10
Choose the statement which most correctly describes the distribution of the
waiting times for a monorail at Disney World.
A.
B.
C.
D.
E.
10.
The mean waiting time was 9.45 minutes.
No-one had to wait more than 15 minutes.
50% of people waited more than 9.45 minutes.
More than 75% of people waited more than 10.95 minutes.
25% of people waited between 7.55 and 10.95 minutes.
A marketing consultant observed 50 shoppers at a supermarket. One variable
of interest was how much each shopper spent in the store. The amounts (in
dollars) spent in the store by the 50 shoppers were organised into the following
frequency distribution using Excel.
Bin
Frequency
20
30
40
50
60
70
80
90
19
29
14
17
10
4
2
5
0
More
The Excel histogram which most correctly represents the data is given by
A.
Number of Shoppers
Histogram of the Amounts Spent in a
Supermarket by 50 Shoppers
35
30
25
20
15
10
5
0
10
20
30
40
50
60
70
80
Amount Spent ($)
QBM117 Multiple Choice Test – Spring 2003
Page 6 of 10
B.
Number of Shoppers
Histogram of the Amounts Spent in a
Supermarket by 50 Shoppers
35
30
25
20
15
10
5
0
25
35
45
55
65
75
85
95
Amount Spent ($)
C.
Number of Shoppers
Histogram of the Amounts Spent in a
Supermarket by 50 Shoppers
35
30
25
20
15
10
5
0
15
25
35
45
55
65
75
85
Amount Spent ($)
D.
Number of Shoppers
Histogram of the Amounts Spent in a
Supermarket by 50 Shoppers
35
30
25
20
15
10
5
0
15
25
35
45
55
65
75
85
Amount Spent ($)
QBM117 Multiple Choice Test – Spring 2003
Page 7 of 10
E.
Number of Shoppers
Histogram of the Amounts Spent in a
Supermarket by 50 Shoppers
35
30
25
20
15
10
5
0
20
30
40
50
60
70
80
90
Amount Spent ($)
11.
A box of marbles contains 3 white marbles, 4 black marbles, and 1 blue
marble. If two marbles are selected at random, what is the probability of
selecting 1 white marble and 1 blue marble (without replacement)?
A.
B.
C.
D.
E.
3 1

8 7
3 1 1 3
  
8 7 8 7
3 1 1 3
  
8 8 8 8
3 1

8 8
Can't be done, as there is only one blue marble.
Use the following information to answer questions 12. and 13.
It is estimated that the probability that a student will pass a subject is 0.8 and we
assume that whether a student passes the subject or not is independent of whether
other students pass the subject. In a class of 15 students,
12.
Find the probability that exactly 12 will pass the subject.
A.
B.
C.
D.
E.
13.
0.250
0.602
0.352
0.750
none of the above.
Find the probability that at least 10 will pass the subject
A.
0.164
B.
0.061
C.
0.939
D.
0.836
E.
0.188
QBM117 Multiple Choice Test – Spring 2003
Page 8 of 10
14.
A shipping company can unload 8 ships per week and the average number of
ships arriving each week is 6. If the total number of ships arriving per week is
8 or less the shipping manager does not have to pay overtime, if the number
exceeds this the manager has to pay overtime, so that there is not a backlog for
next week. Assuming the ships arrive randomly and independently. Find the
probability that the manager will have to pay overtime for the week.
A.
B.
C.
D.
E.
15.
A football team plays 55% of their games at home and 45% of their games
away. Given that the team has a home game, there is a 80% chance they will
win. Given that it is an away game, there is a 65% chance that they will win.
If the team wins what is the probability that they played at home.
A.
B.
C.
D.
E.
16.
0.32
0.58
0.90
0.40
0.70
Given that z is the standard normal variable, find P(0.6  z  2.6)
A.
B.
C.
D.
E.
18.
55%
80%
65%
44%
60%
If P ( A / B)  0.8 , P ( A)  0.5 , and P ( B )  0.4 , then the P( A or B) is:
A.
B.
C.
D.
E.
17.
0.084
0.847
0.916
0.153
0.069
2
0.2257
0.7210
0.2696
0.4953
Given that z is the standard normal variable, find a if P( z  a)  0.8599
A.
B.
C.
D.
E.
1.08
-1.08
0.36
-0.36
0.3599
QBM117 Multiple Choice Test – Spring 2003
Page 9 of 10
19.
If X is normally distributed with mean   5 , and standard deviation   2 ,
then P(2  X  8) is
A.
B.
C.
D.
E.
20.
0.8664
0.4332
0.0668
0.1336
0.6332
A sample of size 16 is drawn from a population which is normally distributed
with a mean of 20 and a standard deviation of 8. What is the probability that
the sample will have a mean greater than 22.
A.
B.
C.
D.
E.
0.0987
0.1587
0.3413
0.4013
0.6587
QBM117 Multiple Choice Test – Spring 2003
Page 10 of 10