Business Mathematics & Statistics Worksheets - (S-203) Spring (Summer) 2009 Examinations - Institute Of Cost And Management Accountants Of Pakistan Page 2
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1
2
3Marks
Q. 3
(a)
The function describing the marginal cost (in rupees) of producing a product is:
MC = 8x + 800
Where x equals the number of units produced. It is known that total cost equals
Rs.80,000, when 40 units are produced. Determine the total cost function.
05
2
(b)
05
Determine the derivative of f(x) = 5x
– 3x + 5 by using limit approach method.
(c)
Determine the monthly car payment necessary to repay a Rs.300,000 car loan, if
the interest is 18% per year compounded monthly. Assume the period of loan is 5
years. Find the amount of interest.
08
60
(Note: 1.015
= 2.44322)
(d)
02
Find the mid-point of the line segment connecting the points (2, 4) and (–3, 6).
SECTION - B
Q. 4
(a)
The mean and variance of 5 observations are 7.4 and 12.64, respectively. If 3 of the
5 observations are 2, 8 and 12, find the remaining two observations.
05
(b)
The grades of a class of 9 students on a midterm report (x) and on a final
examination (y) are as follows:
x
40
20
25
20
30
50
40
55
45
y
85
40
95
65
75
44
49
65
55
Required:
04
(i) Compute and interpret coefficient of correlation.
01
(ii) Compute and interpret coefficient of determination.
Q. 5
(a)
A class has 20 boys and 16 girls, of which, half the boys and half the girls are fat.
Find the probability that a student chosen, at random, is:
(i) either a boy or a fat student.
2.5
2.5
(ii) either a girl or a fat student.
(b)
The weights of a large number of miniature poodles are approximately normally
distributed with a mean of 8 kilograms and standard deviation of 0.9 kilogram. If
measurements are recorded to the nearest tenth of a kilogram, find the fraction of
these poodles with weights between 7.1 and 9.2 kilograms inclusive.
05
SECTION – C
Q. 6
(a)
Calculate the cost slopes and the critical path of the following network:
05
Preceding
Time
Cost (Rs.)
Activity
Activity
Normal
Crash
Normal
Crash
1
6
4
5,000
6,200
–
2
4
2
3,000
3,900
–
3
1
7
6
6,500
6,800
4
1
3
2
4,000
4,500
5
2, 3
5
3
8,500
10,000
(b)
Construct a least cost schedule for the network in part (a) showing all durations from
normal time – normal cost to crash time – crash cost.
05
2 of 3
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