SESSIONAL EXAMINATIONS

Extracted Content: SESSIONAL EXAMINATIONS

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MIDLANDS STATE UNIVERSITY

FACULTY OF COMMERCE

DEPARTMENT OF ACCOUNTING

QUANTITATIVE ANALYSIS OF BUSINESS:
(ACC 102)
SESSIONAL EXAMINATIONS

MAY/JUNE 2016
TOTAL MARKS: 100 MARKS
DURATION: 3 HOURS

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INSTRUCTIONS

1. Answer any FIVE questions.

2. Begin an answer to a new question on a new
page.

3. This paper has FOUR printed pages.

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Provide Formulac booklet and standard normal distribution table.

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Question 1 (20 marks) The distance travelled (in km) by a taxi on 30 trips were recorded by the driver as follows:

24 19 21 27 20 17 17 32 22 26
18 13 23 30 10 13 18 22 34 16
18 23 15 19 28 25 25 20 17 15
a)Define the random variable, the data type and the measurement scale (3 marks)
b)Prepare an absolute frequency distribution (7 marks)
c)Construct a well labelled bar graph. (10 marks)
Question 2 (20 marks)

TelOne has implemented a system of charging out telephone calls based on the length of call.
To find out how this new charging out system would affect its telephone bill, a market survey
was carried out over a period of 3 days monitoring the duration of 600 calls made by its
clients. The following frequency distribution was compiled:

Duration Number

(minutes) of calls

2-<5 38

5-<8 122

8-<11 186

11-<14 134

14-<17 98

17-<20 22
i)Find the mean of call length (3 marks)
ii) Find the median of call length (3 marks)
iii) Find the standard deviation of call length (3 marks)
iv)Establish the interquartile range (4 marks)
v) Establish the values of Pearson’s skewness measure @ marks)
vi) Establish the values of Bowley’s skewness measure (4 marks)
Interpret your calculations where possible.
Question 3 (20 marks)

The Human Resources department of Prostar Insurance firm analysed the qualifications
profile of their 129 managers. The qualification level is the highest qualification achieved by
a manager. The results are as follows:

Qualification Management level
level

Section Head | Departmental Head | Division

Head

A’ level 28 14 Cc
Diploma 20 24 6
Degree A 10 14
Total 53 B 28
Required
a)
i) Define the two random variables and data type (2 marks)
ii) Calculate a,b and c in the above (3 marks)

iii) What is the probability of a person selected at random:

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b)having only an A’ level? (1 mark)

c) being a section head and having a degree? (2marks)
d)being a departmental head given that they have a diploma? (4marks)
e)being divisional head or a section head? (3 marks)
fhaving an A’ level,or a diploma or a degree? (1 mark)
g)having A’ level given that the person is a departmental head? (3 marks)
h) Are the events in (e ) above mutually exclusive? Why? (1 marks)

Question 4

a)Give any two characteristics of a continuous random variable? (2 marks)

b) Give any three continuous random variables. (3 marks)

c)Determine the missing values for the following probabilities involving the standard normal
distribution. Each determination carries 3 marks.

i)P(O<z<?) =0,4015

ii)P(?<z<0) = 0,4803

iti)P(?<z) = 0,0985

iv)P(z<?)_ =0,7517

v)P(?<z) = 0,6331

Question 5 (20 marks)
A company which supplies ready to drink beverages receives, on average, 6 orders per
day.
a) What is the probability that on a given day:
(i ) No orders will be received? (2 marks)
(ii) No more than 2 orders will be received? (3 marks)
(iii) At least 3 orders will be received? (3 marks)
b) What is the probability that, on a given half-day, no orders will be received?(3 marks)
c) What is the mean and standard deviation of orders received per day? (4 marks)

d) Certain tablet are packed 12 per box. If 5% of the tablets manufactured are cracked,
what is the probability that a randomly selected box will:

(i) Be free of cracked tablets? (2 marks)
(ii) Have not more than one cracked tablet? (3 marks)
Question 6 (20 marks)

a)Find the degree of association (Pearson’s correlation coefficient=r) between Gweru City
Council valuations and Market values. Is this a good association? Comment. (10 marks)

Council values Market values
12 65
45 220
32 142
| 50 310
28 196
56 364
18 116
40 260
b) Find r’ and comment (2 marks)

c) Calculate the exogenous factors in this association and comment, (2 marks)

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d) Present the data on a scatter diagram. (6 marks)

THE END OF PAPER

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