Download FUNDAMENTALS OF BUSINESS STATISTICS

INSTITUTE OF BANKERS IN MALAWI
CERTIFICATE IN BANKING EXAMINATION
SUBJECT: FUNDAMENTALS OF BUSINESS STATISTICS
(IOBM – C103)
Date: Monday, 5th November 2012
Time Allocated: 3 hours (08:00 – 11:00 am)
INSTRUCTIONS TO CANDIDATES
1
This paper consists of TWO Sections, A and B.
2
Section A consists of 4 questions, each question carries 15 marks.
Answer ALL questions.
3
Section B consists of 4 questions, each question carries 20 marks.
Answer ANY TWO questions.
4
You will be allowed 10 minutes to go through the paper before the start of
the examination, you may write on this paper but not in the answer book.
Begin each answer on a new page.
5
6
Please write your examination number on each answer book used.
Answer sheets without examination numbers will not be marked.
7
DO NOT open this question paper until instructed to do so.
A qualification examined by the Institute of Bankers in Malawi
Page 1
SECTION A
(60 MARKS)
For items 1), 2), and 3):
450
Cumulative number of
Employees
400
350
300
250
200
150
100
50
0
0
10
20
30
40
50
60
Age in Years
1)
2)
3)
The graph is called
a.
a frequency distribution
b.
an ogive
c.
frequency polygon
d.
histogram
The inter-quartile range of the distribution is approximately
a.
100
b.
35
c.
300
d.
10
Which of the following statements are true?
a.
About 300 employees are younger than 30.
b.
25% of the employees are older than 45.
c.
The inter-quartile range represents 60% of the employees.
d.
75% of the employees are younger than 35.
A qualification examined by the Institute of Bankers in Malawi
Page 2
4)
A sample of employees who completed a training were asked to rate it as
either outstanding, very good, fair, or poor. The level of measurement
used is:
5)
a.
nominal
c.
ordinal
b.
interval
d.
ratio
The strength of association between an independent variable and a
dependent variable is measured by the:
a.
coefficient of determination
c. coefficient of variation
b.
correlation coefficient
d. regression coefficients
For items 6), 7), 8) and 9): A random sample of new graduates in “banking”
indicates that their salaries (MK’000) are as given below.
6)
7)
8)
9)
39.5
59.4
45.1
51.2
55.8
26.7
65.6
62.6
48.7
28.5
21.6
78.4
34.9
50.9
53.6
30.6
53.9
32.3
34.1
36.2
The median salary of the sample is
a.
K45, 100
c. K45, 470
b.
K46, 900
d. K47, 870
The mean salary of the sample is
a.
K45, 100
c. K45, 480
b.
K46, 900
d. K47, 870
The standard deviation of the distribution, to the nearest K100, is
a.
K14, 600
c. K15, 480
b.
K14, 500
d. K15, 000
The coefficient of skewness of the distribution is
a.
-0.3
c. 0.3
b.
-0.1
d. 0.1
A qualification examined by the Institute of Bankers in Malawi
Page 3
10)
A useful measure to compare the relative dispersion of two or more
distributions, if they are in different units, is the
11)
a.
coefficient of skewness
c. coefficient of variation
b.
mean deviation
d. standard deviation
If distribution gives the following statistical summaries: mean = 100,
median = 100, mode = 100 and standard deviation = 4, then the
distribution can be said to be
12)
a.
positively skewed
c. negatively skewed
b.
symmetrical
d. asymmetrical
Almost all the data values in the distribution given in item 11) above fall
within the range
a.
-4 to 4
c. -3 to 3
b.
96 to 104
d. 88 to 112
For items 13) and 14): If two variables x and y are such that 𝑦 = 12 − 0.5𝑥,
13)
14)
15)
The product moment correlation coefficient between x and y is
a.
0.5
c. -1
b.
1
d. -0.5
The y-intercept is
a.
0
c. -0.5
b.
12
d. 0.5
You divide a region into constituencies. Then you sample 12
constituencies at random and concentrate your participant-selection
efforts in those constituencies. This type of sampling is
a.
simple random sampling
c. stratified sampling
b.
systematic sampling
d. cluster sampling
A qualification examined by the Institute of Bankers in Malawi
Page 4
For items 15), 16) and 17): The following histogram shows the distribution of the
difference between “actual” and “ideal” account balances for 119 female
students.
35
30
Percent (%)
25
20
15
10
5
0
-20 -15 -10 -5
0
5
10
15
20
25
30
35
40
45
50
55
Difference = Actual - Ideal
16)
17)
18)
19)
What is the approximate shape of the distribution?
a.
nearly symmetric
c. skewed to the left
b.
skewed to the right
d. bimodal
The median of the distribution is approximately
a.
-10
c. 30
b.
10
d. 50
The actual account balances of most of the female students were:
a.
about the same as their ideal balances
b.
less than their ideal balances
c.
greater that their ideal balances
d.
exactly the same as their ideal balances
The coefficient of determination was computed to be 0.25 in a problem
involving an independent variable and a dependent variable. This result
means
A qualification examined by the Institute of Bankers in Malawi
Page 5
a.
the variables are positively correlated
b.
the correlation coefficient is 0.0625
c.
the correlation coefficient is ±0.5
d.
25% of the variability in the independent variable is explained by
the dependent variable.
For items 20), and 21): A survey asked bank customers how often they use the
bank’s ATM. The results are summarised in the contingency table below.
20)
Age (Years)
Often
Not often
Below 25
30
60
25 but below 40
90
100
Over 40
20
100
Among the customers aged below 25, what is the likelihood of using the
ATM often?
21)
a.
0.33
c. 0.21
b.
0.08
d. 0.50
What is the probability that a randomly selected customer is over 40 and
does not often use the ATM.
22)
23)
a.
0.25
c. 0.14
b.
0.17
d. 0.05
Which one of the following variables is not categorical.
a.
Age of a person
b.
Gender of a person
c.
Nationality of a person
d.
Marital status of a person
Which one of these statistics is not sensitive to outliers?
a.
Mean
c. Standard deviation
b.
Inter-quartile range
d. Range
A qualification examined by the Institute of Bankers in Malawi
Page 6
24)
How would an outlier affect the value of a correlation coefficient?
a.
It will always reduce the value of a correlation coefficient
b.
It will always increase the value of a correlation coefficient
c.
It will have no effect on the value of a correlation coefficient
d.
It will either reduce or increase the value of a correlation coefficient,
depending on its relative position.
25)
To conduct a survey on ATM usage, a bank manager opens a printout to a
random page, closes her eyes, puts a finger down on the page and then
gets details of the next 5 customers. Which of the following statements are
true?
I. The survey incorporates chance.
II. The procedure results in a simple random sample.
III. The procedure could easily result in selection bias
26)
a.
I. and II.
b.
I. and III.
c.
I., II. and III.
d.
None of the above.
The total costs (K’ million) of importing 5 cars through the bank in January,
2012 gave the following summaries:  x  30.7 ,  x 2  205.31
The standard deviation (K’ million) for the costs is:
a.
1.83
c. 4.20
b.
2.05
d. 16.81
For items 27) – 30): In a group of 75 Blantyre residents, 15 play pool, 50 play
loto 36, 10 play both, and 20 play neither. Suppose a Blantyre resident is chosen
at random from this group. Let A be the event “a resident plays pool”, and B be
the event “a resident plays loto 36”.
A qualification examined by the Institute of Bankers in Malawi
Page 7
27)
28)
29)
30)
Events A and B are:
a.
independent and mutually exclusive
b.
independent, but not mutually exclusive
c.
mutually exclusive, but not independent
d.
neither mutually exclusive nor independent
What is the probability that the resident plays pool or loto 36?
a.
1.00
c. 0.73
b.
0.60
d. 0.87
What is the probability that the resident plays pool but not loto 36?
a.
0.07
c. 0.27
b.
0.20
d. 0.33
What is the probability that the resident does not play loto 36?
a.
0.07
c. 0.27
b.
0.20
d. 0.33
A qualification examined by the Institute of Bankers in Malawi
Page 8
SECTION B
(40 MARKS)
Answer ANY TWO questions from this section.
QUESTION 31
a)
State one main disadvantage of the mean.
(2 marks)
b)
The following is a frequency distribution of the total annual premiums for
motor vehicle insurance made out by a sample of 100 local companies.
Annual Premiums
(K’000)
0 – 200
200 – 400
400 – 600
600 – 800
800 – 1000
1000 – 1200
Number of
Companies
15
28
32
15
6
4
Calculate the following statistics:
i.
Mean
(4 marks)
ii.
Median
(5 marks)
iii.
Standard deviation
(6 marks)
iv.
Coefficient of skewness and comment on the value obtained.
(3 marks)
(Total 20 marks)
A qualification examined by the Institute of Bankers in Malawi
Page 9
QUESTION 32
a)
Distinguish interpolation from extrapolation in the context of regression
analysis.
(4 marks)
The data below show monthly incomes (K’000) and monthly house rentals
b)
(K’00) for a sample of families from Lilongwe.
i.
Income (x)
16
45
36
32
30
13
41
15
36
40
Rental (y)
35
78
102
56
75
26
130
42
59
85
Find the equation of the least squares regression line that relates
income and house rental.
ii.
(8 marks)
Calculate the Pearson correlation coefficient between x and y and
comment on the value obtained.
iii.
(5 marks)
Use the regression equation found in i. to predict monthly house
rentals for a family whose monthly income is K30,000.00.
iv.
(2 marks)
By how much will the monthly rentals change if the family income
increases by K1,000.00?
(1 marks)
(Total 20 marks)
A qualification examined by the Institute of Bankers in Malawi
Page 10
QUESTION 33
a) A company decides to tender for 3 contracts; A, B and C. The probability that
it will obtain contract A is 0.5, contract B is 0.4 and contract C is 0.3. The
contracts are awarded independent of one another. Calculate the probability
that it will get:
i.
no contracts
ii.
only one contract.
(3 marks)
(4 marks)
b) A manager decided to check the accuracy of invoicing in its system. Invoices
are prepared by 3 clerks, Chloe, Entire and Zoe. A sample of 1,000 invoices
was selected. 300 were prepared by Chloe, 300 by Entire and 400 by Zoe.
The error rates for Chloe, Entire and Zoe are estimated to be 2%, 5% and
3% respectively. From the sample of 1,000 invoices, one was selected.
Calculate the probability that it:
i.
was prepared by Chloe
(2 marks)
ii.
contained an error
(4 marks)
c) A fruit juice company produces fruit juice in 10 different flavours. A local
supermarket sells the juice, but has only sufficient shelf space to display
three of the company’s 10 fruit juice flavours.
i.
How many different groups of three flavours can be displayed on the
shelf?
ii.
(3 marks)
Suppose that one of the flavours is Banana. What is the probability that
the Banana flavoured juice will be displayed?
A qualification examined by the Institute of Bankers in Malawi
(4 marks)
Page 11
QUESTION 34
a) The data below shows the cumulative distribution of income among
employees of a local company
Highly paid (%)
1
5
10
25
50
All
Gross income (%)
17
38
53
75
94
100
Net income (%)
10
24
36
60
83
100
Note: The data is cumulative, e.g. the most earners 5% includes the most earners 1%
i.
On the same graph, plot Lorenz curves for gross income and net income.
(6 marks)
ii.
Briefly comment on the effect of tax on the distribution of income among
the employees.
(2 marks)
b) The table below shows deposits (in K’million) made at a certain service
centre of a bank located in a rural setup.
Month, 2011
July
August
September
October
November
December
January
February
March
April
May
June
i.
Actual deposits
5
1
4
10
3
6
8
1
4
1
8
3
12-months moving totals
46
44
49
48
51
49
53
54
55
53
56
54
Represent the data on a Z-chart. (Use a scale of 2cm:K10 million on the yaxis)
ii.
(8 marks)
Interpret the two larger values corresponding to October, 2011 on your zchart.
A qualification examined by the Institute of Bankers in Malawi
(4 marks)
Page 12