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DIPLOMA EXAMINATION, 2011
(quality management)
(pAPer–ii)
120. fundamentals of statistics and costing
May) (Time: 3 Hours
Maximum: 100 Marks
Answer ALL questions (5×20=100)
All questions carry equal marks
1. / a) The following data pertain to marks obtained by 120 students in their final examinations in mathematics:Marks / Number of students
90-100 / 09
80-89 / 32
70-79 / 43
60-69 / 21
50-59 / 11
40-49 / 03
30-39 / 01
Total / 120
Calculate the lower and upper quartiles
b) For a group containing 100 observations, the arithmetic mean and the standard deviation are 8 and , respectively. For 50 observations selected from these observations, the mean and the standard deviation are 10 and 2, respectively. Find the mean of the remaining 50 observations.
(OR)
2. / In two factories A and B engaged in similar type of industry, the average weekly wages and standard deviations are as given below:
Factory A Factory B
Average weekly wages (Rs.) 460 490
Standard deviation of weekly wages (Rs.) 50 40
Number of wage - earners 100 80
(i) Which factory shows greater variability in the distribution of weekly wages?
(ii) What is the mean of all the workers in two factories together?
(iii) Given the following distribution, calculate and plot ‘less than’ frequency curve.
[Continues....
Class / Frequency
40-49 / 4
50-59 / 8
60-69 / 4
70-79 / 24
80-89 / 6
90-99 / 4
3. / a) In testing a certain kind of truck tire over a rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blow out. Of the next 15 trucks tested, find the probability that (i) from 3 to 6 have blow outs (ii) fewer than 4 have blow outs.
b) On the average a certain intersection results in 3 traffic accidents per month. What is the probability that in any given month at this intersection (i) exactly 5 accidents will occur? (ii) Less than 3 accidents will occur.
(OR)
4. / a) The finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.03 centimeter.
(i) What proporation of rings will have inside diameters exceeding 10.075 centimeters?
(ii) What is the probability that a piston ring will have an inside diameter between 9.97 and 10.03 centimeters?
b) The probability that a contractor will get a plumbing contract is 2/3 and the probability that he will not get an electrical contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that he will get both the contracts.
5. / a) Describe the procedure involved in the one way analysis of variance.
b) Explain the following:
(i) signal – to – noise ratio
(ii) blocking
(iii) noise factors
(iv) replications
(OR)
6. / Three different methods of teaching statistics are used on three groups of standards. Random samples of size 5 are taken from each group and the results are shown below. The grades are on a 10 point scale.
Group A / Group B / Group C
7 / 3 / 4
6 / 6 / 7
7 / 5 / 7
7 / 4 / 4
8 / 7 / 8
[Continues......
Determine on the basis of the above data whether there is a difference in the teaching methods.
7. / Potential locations A, B and C have the cost structures as shown below for producing a product expected to sell for Rs.3,250 per unit. Find the most economical location for an expected volume for 2,750 units per year.
Size / Fixed cost / year (Rs.) / Variable cost / year (Rs.)
A / 65,00,000 / 1,200
B / 75,00,000 / 560
C / 55,00,000 / 4,250
(OR)
8. / A manufacturing firm has three proposals for a product. Either it can be purchased from an outside vendor at Rs.4 per unit or it can be manufactured in plant. There are two alternatives for in-plant manufacturing. Either, a fully automatic unit is procured, involved a fixed cost of Rs.30,000 and a variable cost of Rs.2.75 per unit. Alternatively, a semi-automatic unit would cost Rs.20,000 as fixed cost and Rs.3 per unit as variable cost. Draw a break-even-chart for these alternatives. Suggest range of production volume suitable for these alternatives.
9. / a) What is standard costing? What are its advantages, limitations and applications?
b) Explain process costing. In what type of industries is process costing generally adopted? Also distinguish between job-order costing and process costing.
(OR)
10. / Write short notes on:
(i) Job costing (ii) Batch costing (iii) Activity based costing.
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