Upload
ravindra-babu
View
236
Download
1
Embed Size (px)
Citation preview
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 1/16
REVISION- BUSINESS MATHEMATICS AND
STATISTICS - RBTWO MARKS QUESTIONS:
1. What is meant by degrees of freedom?
2. When does the arithmetic mean lose its significance?
3. Differentiate between a census and a survey?
4. Illustrate symmetrical and asymmetrical distributions.
5. Find the 5th term and the sum of the first 8 terms of an AP 1,10,19,.....
6. Explain “level of significance”
7. What is the significance of a null hypothesis
8. Distinguish between ‘maxima’ and minima
9. List out the characteristics of statistics
10. What are the limitations of binomial distribution?
11. What is decision making under uncertainty?
12. What are the advantages of stratified random sampling?
13. What is standard error?14. What is index number
15. What is correlation
16. What is regression
17. What is dispersion? What is the purpose of a measure of dispersion?
18. What is Skewness? What are the different measures of skewness?
19. How will you interpret the sign and magnitude of a correlation coefficient?
20. List the chief properties of a normal distribution.
21. What is a sign test? When is it used?
22. In which context is the Mann Whitney Test used?
23. What is kurtosis? Explain the three different curves under kurtosis?
24. What is binomial distribution? What are its business applications?
25. Give one example for each of the following: i) Linear function ii) Geometric Progression.26. What is meant by the regret criterion?
27. Find the sum of the first 10 terms of an A.P 1,4,7,10.....
28. Find the sum of the first 12 terms of an A.P 1,3,5,7........
29. Find three numbers in A.P whose sum is 21 and product is 280?
30. What term of the following A.P 3 + 6 + 9 + 12....... is 90.
31. The fourth term of a G.P is ½ and the seventh term is 4/27. Find the 12th term.
32. The 3rd term of a G.P is ¾ and the seventh term is 4/27. Find the fourth term
33. Find the sum of the series 3+7+11..... to 40 terms.
34. How many terms of a G.P 4,2,1 amount to 127/16?
35. The first term and the last term of a G.P are 4 and 324. The sum of the series is 384.
Find the CR.
36. What is the importance of statistics in managerial decision making?
37. What are averages? How are they useful?
38. What is Sampling? Jan 05
39. What is Chi square test? Where and for what it is used?
40. What are the components of Time series
41. What is correlation? Mention its significance
42. What is sum of squares and mean of squares
43. What is the significance of testing a hypothesis
44. What is Poisson distribution
45. What is Sign Test
46. What are Index Numbers
47. What is Binomial Distribution48. What is cluster Sampling
49. Define Integration
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 2/16
Eight Marks Questions and Twelve Marks
Theory Questions
1. Why is statistics called imposing mathematics
2. What do you mean by sampling errors? Explain the types of sampling errors?
3. Is it important for the chosen samples to be representative of the population. Using thevarious methods of sampling, explain how representativeness can be achieved
4. Eloborate on how a decision tree and the payoff-EMV concepts are useful in
managerial decision making.
5. Explain the applications of statistics in managerial decision making. Also discuss the
limitations of statistics.
6. What is Sampling? Why is it important? Discuss the methods of Sampling?
7. Explain the procedure of setting up and testing a hypothesis? [Jan 05,06]
8. What is decision tree? What are the steps in decision tree analysis? [Sep 01, Jan-07]
9. Explain addition, subtraction and multiplication of matrices with examples.
10. What is a statistical average? State the properties of a good average.
11. Explain the method of moving averages in calculating the trend. What are the meritsand limitations of this method.
12. Explain the procedure of setting up and testing a hypothesis.
13. What is business forecasting? Explain the various techniques of forecasting. Explain
the major steps in forecasting. What are the limitations of forecasting?
14. What is correlation? Distinguish between positive and negative correlation. What is
the significance of coefficient correlation?
15.Explain and point out the difference between one tailed and two tailed tests.
16. Explain business forecasting and its various methods. How is it useful to a business
manager?
17. Explain Chi square analysis with an example
18. Explain Annova with an example
19. Explain the terms “level of significance” and degrees of freedom used in Chi Square
test.
20. How is regression and its applicability in business different from correlation and its
applicability
21. Explain the Time Reversal Test and Factor Reversal Test with help of suitable
examples.
22. Distinguish between correlation and regression analysis.
23. Distinguish between Karl Pearson’s and Bowley’s measure of skewness. Which one
of these would you prefer and why?
24.
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 3/16
REVISION- BUSINESS MATHEMATICS AND
STATISTICS - RB1. The following are the annual profits in thousands of rupees, in a certain business:
Year 2001 2002 2003 2004 2005 2006 2007Profits
(Rs 000)
60 72 75 65 80 85 95
i) Use the method of Least square to fit a straight line to the above data
ii) Also make an estimate of the profits for the year 2009 [Jan 2011]
2. Fit the straight line trend by the method of least squares for the following data.
Forecast the production figures for the coming year. A graph is not necessary
[Jan2010]
3. Fit a straight line trend by the method of least square to the following data and the
project the production for the next two years (A graph is not required)
[Jan 2009]
3. ABC Ltd gives the following information relating to the sales of refrigerators in the past
ten years: [Jan 2008]
Fit a straight line trend by the method of least squares and estimate the sales of 2009
4. Fit a straight line trend for the following data: [Jan 2007]
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
Year 200
3
200
4
200
5
200
6
200
7
2008
Production in ‘000 metrictons 140 146 142 145 150 160
Year 200
2
200
3
200
4
200
5
2006
Production in ‘000 metric
tons
45 45 47 48 52
Year 199
8
199
9
200
0
200
1
200
2
200
3
200
4
200
5
200
6
2007
Refrigerators sold
in thousands
8 10 11 11 18 15 19 19 22 24
Year 199
1
199
2
199
3
199
4
1995
Sale of sugars in ‘000 metric tons 80 90 92 93 94
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 4/16
5. Fit a straight line trend by the method of least squares to the data given below and project
the probable sales for the next two years (A graph is not required) [Jan 2006]
6. Calculate Karl Pearson’s and Bowley’s coefficient of Skewness for the marks obtained by
students of 2 institutions [Jan 2010]
7. For a group of 20 items Σ x =
1452, Σ x2 = 144280 and mode = 63.7. Find the Pearsonian’s coefficient of Skewness.
[Jan 2009]
8. Illustrate skewness with diagram given Q1 = 18, Q3 = 35, Mode = 21, Mean = 18, Find
the coefficient of skewness [Jan 2011]
9. Find the coefficient of correlation with the help of Karl Pearson’s Method [Jan 2011]
X 4
3
4
4
4
6
4
0
4
4
4
2
4
5
4
2
3
8
4
0
4
2
57
Y 2
9
3
1
1
9
1
8
1
9
2
7
2
7
2
9
4
1
3
0
2
6
10
10. Find the coefficient of correlation for the following data: [Jan 2010]
X 1
9
2
1
2
3
2
5
32
Y 6
5
6
6
6
5
6
8
75
11. Find the Karl Pearson’s coefficient of correlation, the probable error and comment on the
significance of correlation for the following data: [Jan 2008]
12.Calculate the
coefficient of correlation
and the probable error and comment on the significance of correlation for the following data:
[Jan 2009]
X 6 7 7 9 1
0
12
Y 18
16
17
19
19
21
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
Year 199
9
200
0
200
1
200
2
200
3
2004
Sales in thousands of Rupees 164 180 186 187 190 192
Measure Institution A Institution B
Mean 65 66
Median 61 62
Standard
Deviation
10 13
Third Quartile 87 102
First Quartile 78 30
Advertising expenses 1
5
1
8
1
9
2
0
2
2
2
4
25
Sales in ‘000 Rs 2
4
2
6
2
6
2
7
2
8
2
8
30
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 5/16
13. Obtain the regression equations for the following data: [Jan 2007]
X 3
0
5
0
2
0
80 1
0
2
0
2
0
40
Y 5
0
8
0
3
0
11
0
2
0
2
0
4
0
50
14. An investment company speculates about the relationship between the family incomeand their allocation for investment. A survey of 8 randomly selected families gives the
following data: [Jan 2010]
a) Develop the regression equations to describe this data. b) Estimate the probable income of a family who allocates 22 percent for investment
c) What could be the percentage of income allocated to investment by a family
earning Rs 27,500 per month?
15. Determine the regression equation X on Y and Y on X for the following data:[Jan
2011]
X 1
2
1
4
1
6
2
0
32
Y 3
4
4
0
3
8
4
2
50
16. The following data gives the experience of lathe operations in a factory and the
number of lathe operators in a factory and the number of units of production turned out per
day.
[Jan 05/06]
Lathe Operator 1 2 3 4 5 6 7
Experience in yrs(X) 1
4
1
0
1
6
2 1 8 3
Units of
Production(Y)
8
4
8
0
8
7
6
0
5
4
7
8
56
Calculate the regression lines and
i) Estimate the probable units of production of a lathe operator with an experience of 15 yrsii) Estimate the years of experience of a lathe operator with a daily production of 96 units
17. A manufacturing company purchases plastic buckets which are normally distributed
with a mean diameter of 9 inches and a variance of 3 inches. In a total production of 12,000
buckets how many are expected to be
a) Greater than 12 inches in diameter?
b) Less than 7 inches in diameter?
c) Between 8 inches and 10 inches in diameter? [Jan 2010]
18. The mean and standard deviation of marks obtained by the candidates in a
competitive examination are 50 and 15 respectively it 1200 candidates appear for the
examination. Find:
[Jan 2009]a)The number of candidates who are expected to score more than 70
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
Annual income in 000s 1
8
2
1
1
9
3
4
2
3
3
0
3
6
38
Percent allocation for investment 2
8
3
6
3
2
4
0
3
5
5
5
6
0
64
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 6/16
b)The expected number of candidates who score between 60 and 75 marks.
c) The number of candidates who may score between 35 and 55 marks
d) The number of candidates who score less than 40 marks.
19. An aptitude test for selecting Management Trainees was conducted on 5000
candidates. The average score was 56 and the standard deviation was 24. Assuming normal
distribution for the scores. Find: [Jan 2008]
i) The number of candidates whose scores exceeded 85
ii) Candidates who scored between 65 and 70.
iii) Candidates who scored less than 50
iv) Candidates who scored 60
20. The average monthly sales of 5000 firms are normally distributed. It mean and
standard deviation are Rs 36,000 and Rs 10,000 respectively. Find:
i) The number of firms the sales of which are over Rs 40,000.
ii) Percentage of firms the sale of which will be between Rs 38,500 and 41,000
iii) The number of firms the sales of which will be between Rs 30,000 and Rs 40,000
iv) The number of firms the sales of which are less than Rs 30,000 [Mar 2011] 21. The screws produced by a certain machine were checked by examining number of
defectives in a sample of 12. The following table shows the distribution of 128 samples
according to the number of defective items they contained
No of
defectives
in a
sample of
12
0 1 2 3 4 5 6 7 Total
No of
samples
7 6 19 35 30 23 7 1 128
Fit a Binomial distribution and find the expected frequencies if the chance of the
machine defective is ½. [Jan 2007]
22.A box contains 50 coins numbered from 1 to 50. One coin is drawn at random. Find
the probability that the number on the coin drawn will be a multiple of a) 3 or 9 b) 5
or 7
23. (a) In an AP of 3,9,15,.... find the (i)sum of the first 14 terms and (ii) the twelth term?
(b) P and Q play for a prize of Rs1,00,000. P is to throw a dice first and is to win if he
throws 1. If he fails, Qis to throw and is to win if he throws 1 or 2. If he fails, P is to
throw again and is to win if he throws 1,2 or 3. Find their respective expectations.[Jan11]
24. A sample of 100 dry battery cells tested to find the length of life produced the
following results: µ = 12 hrs, σ = 3 hrs. Assuming that the data are normally distributed.
What percentage of battery cells are expected to have life. I) more than 15 hrs ii) less than
6 hrs iii) Between 10 and 14 hrs [Mar 02]
Given Z 2.5 2.0 1.0 0.67
Area 0.493
8
0.477
2
0.341
3
0.2487
25.In an intelligence test administered to 500 students, the average score was 42 and
standard deviation was 24. Find [Jan 06]a) The number of students whose score exceeded 50
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 7/16
b) The number of students who got a score between 30 and 40
c) The number of students who got a score above 60
26.1000 light bulbs with a mean life of 120 days are installed in a firm. Their length of
life is normally distributed with a standard deviation of 20 days. How many bulbs will
expire in less than 90 days [Mar 03]
27.An MBA graduate is selected for interview in 3 different firms. For the first post,there are 5 candidate, for the second post, there are 10 candidates and for the third
post, there are 9 candidates, what are his chances of getting at least one post?
[Jan 05]
28. Ten percent of the tools produced in a certain manufacturing process turn out to be
defective. Find the probability that in a sample of 10 tools chosen at random, exactly
two will be defective by using (i) Binomial Distribution (ii) the poisson distribution
29. The number of machines malfunctions per shift at a factory is recorded for 180 shifts
and the following data are obtained:
No of
malfunctions
0 1 2 3 4 5 6
No of shifts 8
2
4
2
3
1
1
2
8 3 2
What is a reasonable probability model for this type of data? [Mar 03]
30.Five students P,Q,R ,S and T are given a problem to solve The probabilities are P- 1/3
Q – 1/5, R- 1/6 , S- 1/8 and T – 1/9 of solving the problem. What is the probability
that the problem will be solved. [Jan 2009]
31.A machinery will function only if all its three components P, Q and R are working.
The probability of P failing during one year is 0.15 that of Q falling is 0.05 and that of
R failing is 0.10. What is the probability that the equipment will fail before the end of
the year. [Mar 04]
32.In a post office three clerks are assigned to process incoming mail. The first clerk
process 40%, second 35% and the third 25% of the mail. The first clerk has an error
rate of 0.04, the second has 0.06 and the third has 0.03. A mail selected at random
from a day’s output is found to have an error. The post Master wishes to know the
probability that the mail was processed by the first, second or third clerk respectively.
[Jan 07]
33.A candidate has to be selected for a managerial post with the following
characteristics: [Jan 08]
An MBA degree (probability of getting such a candidate is one in hundred)
Excellent communication (probability is one in fifty)Knowledge of a foreign language (probability is one in eighty)
Experience of working as a manager (probability of getting such a candidate is one
in 20). Find the probability of getting one required candidate.
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 8/16
34.If the opening stock matrix O=
8 361
5321
1 136
, purchase matrix P =
6453
2319
4132
the
sales matrix S =
4623
735 1
9248
. Find the closing stock matrix C
[Jan 10]
35.If A =
857
2 43
9 16
and B =
754
362
193
find 2 A + 3B [Jan 08]
36.If the revenues of a firm are given by matrix?
=
30
100
2575
7550 R
and the costs are
given by the matrix.
15
35
1045
2525
. Find the profit matrix P.
37.If A =
54
32
=
17
3 B . Find X and such that AX = B.
38.Find the inverse of a matrix A =
−−
−
111
232
422
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 9/16
39.Find the inverse of a matrix A =
751
062
123
40.Find the inverse of a matrix A =
−
−
872
051
436
41.If the opening stock matrix is
24
53, the closing stock matrix is
23
32the sales
unit matrix is
43
34
the sales price per unit is Rs 2 per unit, find the purchases
matrix.
42.If the cost C = 8 x3 + 6 x2+ 3x find the a) average cost b) the marginal cost if the
Quantity produced is 300 units. If the price per unit for sales is as 750, what is the
profit or loss in the sale.
43.Find the maximum and minimum values of the function y = x4 - 8 x2 + 12.
44.If the total cost function C = 4Q - Q2+ 2 Q3 find the average cost function and
marginal cost function. If Q = total quantity.
45.The total cost of x units is y rupees where y = x27.5x0.2-3000
2
3
+ x
and all units
made are sold at Rs 10 per unit. At what two points does marginal cost equals
marginal revenue.
46.From the following information determine the units to be manufactured in order to
earn maximum profits: Tc = 0.0008 X2 + 3.4 X + 25,000 and TR = 0.001 X2 + 25 X
47.A firm produces a single product and it can market as many units as it is able to produce at a price of Rs 1.75. Its plant and equipment can produce as many as 5000
units a day. The total fixed cost is its 2,000 daily. Unit variable cost is Rs 0.50. How
many units per day must be produced in order that the firm breaks even?
48. What is sampling? When is sampling done? Discuss the different methods of
sampling and their applicability in business.
49. A sample of 200 people with particular disease was selected. Out of these, 100 were
given a drug and the others were not given any drug. The results are as follows
Test whether the drug is effective or not [Jan 07]
Number of People
Drug No drug
Cured 65 55
Not Cured 35 45
50.2000 families of a city were selected at random to test belief that families with higher
income bought the sedan-type of car and families with lower income bought the small
car. Given the following results, Use chi square test to find out if it is true: [Jan 06]
Income Sedan type of
car
Small Car Total
High 594 606 1200
Low 262 538 800
Total 856 1144 2000
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 10/16
51.Using Chi-square analysis, determine the incidence of accidents caused by technically
skilled and unskilled personnel. [Jan 05]
Personnel Accidents No accidents Total
Skilled 10 90 100
Unskilled 15 65 80Total 25 155 180
52.Using Chi-square Analysis, determine the incidence of Job-related conflicts caused by
trained and untrained personnel. [Mar- 04]
Personnel Conflict
s
No conflicts Total
Trained 20 180 200
Untrained 30 130 160
Total 50 310 360
53. The expenditure of 1000 families is given as under:
Expenditure in Rs 40-
59
60-
79
80-
99
100-
119
120-139
No of customers 50 X1 500 X2 50
The median and mean for the distribution are both Rs 87.50. Calculate the missing
frequencies
54. Given the following frequency distribution of sales in a departmental store compute
(i) the median, and ii) The quartile deviation. What is the range of sales which contains the
middle of 50% of the receipts?
Sales in rupees 50-99 100-
149
150-159 200-249 250-299 300-
349
Total
No of customers 9 21 42 17 6 5 100
55.Calculate the consumer price Index by the method of (a) Aggregate expenditure and
(b) Family budget for the given data: [Mar 2011]
Commodity Quantity in
2009
Price in 2009 Price in 2010
A 100 8 12.00
B 25 6 7.5
C 10 5 5.25
D 20 48 52.00
E 25 15 16.50F 30 9 27.00
56.Using the following show that Fisher’s Index satisfies time reversal and factor
reversal test. [ Jan 09]
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
Items 200
5
2007
Price Quantity Price Quantity
P 5 6 6 7
Q 7 12 6 13
R 6 15 8 15
S 8 10 8 12
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 11/16
57.Construct Laspeyre’s , Paasche’s and Fisher’s Index for the following data:[Jan 07]
58.Calculate Fischer’s ideal index from the following data and prove that it satisfies the
time reversal and factor reversal tests:
[Jan 05]
59. Calculate
Fischer’s ideal index from the following data and prove that it satisfies the time
reversal and factor reversal tests: [Jan 06]
TWELVE MARKS
QUESTIONS:
1. Infer whether there is a significant variation in the preference for sweet or salty snacks
in different cities from the following data elicited with the sample. [Jan 10]
Bangalore Mumbai Chennai Kolkota
Sweet Snacks 624 987 523 842
Salty Snacks 365 482 650 9622. A study was carried out on the advertising methods of a brand of product. The unit
sales achieved by five stores were recorded as under: [Jan 09]
Calculate the F-ratio, using the Annova and 5% level of significance. Establish
Whether a) four methods of advertisement produce different effects on the sales
volumes b) there is a significant difference between the sales in the different stores.
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
Items 1987 1988
Price Quantity Price Quantity
A 2 8 4 6
B 5 10 6 5C 4 14 5 10
D 2 19 2 13
Items 2001 2002
Price Expenditure Price Expenditure
A 10 55 14 80
B 12 65 16 50
C 8 40 10 60
D 16 80 18 70
E 14 70 12 95
A B C D E
P0 30 32 30 31 32
Q0 95 11
5
12
0
12
5
125
P1 22 24 25 27 28
Q1 21
5
22
0
21
9
22
2
224
Store A Store B Store C Store D Store E
Method I 78 85 82 88 79
Method II 93 87 85 85 85
Method III 81 92 77 83 81
Method IV 79 83 71 78 78
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 12/16
3. Four judges of a soft skills assessment test gave the following marks to six candidates.
Using ANOVA test whether there is a significant differences in [Jan 08]
a) The performance of the six candidates b)The judgement of the four judges
4. The following represent the number of units of production per day turned out by 4
different workers using different types of machines [Jan 07]
Machine Type
WORKERS A B C D E
1 4 5 3 7 6
2 6 8 6 5 43 7 6 7 8 8
4 3 5 4 8 2
On the basis of this information, can it be concluded that
a) The mean productivity is the same for different machines
b) The worker’s don’t differ with regard to productivity?
6. Using the Chi Square test, analyse the following data to determine whether the
preference pattern of consumers for cell phones is dependent on income levels
Cell Phones Low Medium High Total
Nokia 65 90 100 255
Motorola 35 40 80 155
Erricson 50 60 220 330
Total 150 190 400 740
7. A clinical trial gave the following results for a certain experiment conducted in using
a new treatment for curing cold. Using the Chi square test determine whether the
new treatment was attractive or not. [Jan 10]
7. KMF wishes to test whether the preference pattern of Bangalore consumers for
different kinds of milk is dependent on income levels. A random sample of 1200
consumers gives the following data. Use the Chi-square test and determine whether the preference patterns are independent of income levels. [Jan 08]
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
Judges A B C D E F
1 11 12 11 12 13 13
2 13 13 11 13 12 12
3 3 12 12 14 13 12
4 14 15 13 16 14 12
Treatment Favourable
Response
No Response Total
New 265 185 450
Conventional 375 115 490Total 640 300 940
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 13/16
8. A business man from Chennai wishes to sell his products in Bangalore he can set up a
showroom in the city or can sell through a wholesaler, setting up a showroom in the
city will entail costs of Rs 6,00,000 with a 55% probability success. If the showroom
succeeds he can gain a net profit of Rs 10,00,000 per year. If it fails he can either
shutdown the showroom or rent it out for an annual rent of Rs 3,60,000(for the rest
of the year). The probability that he gets rent for the showroom is 40%.
If he sells through a wholesaler he incurs Rs 3,00,000 initial costs. The chances of
selling successfully are 45% with a net profit of Rs 5,50,000 per year.a) Advice the businessman on the best decision
b) How is the decision tree analysis useful in business decision [Mar 04]
9. A businessman has two options to sell his products. He can set up a showroom in the
city or can sell from his factory outlet. Setting up a showroom will cost Rs 3,00,000
with a 60% probability of success. If the showroom succeeds, he can close the
showroom or rent it out for an annual rent of Rs 2,40,000( for the rest of the year).
The probability of getting rent is 80%. [Jan05]
If he sells from the factory outlet, he has to incur Rs 50,000 as renovating charges.
The chances of successful selling here is 40% with a net profit of Rs 4,00,000 per
year
a) What would you advice the businessman to do b) Advise the businessman on how a decision tree helps him to make a decision.
10. An investor has 3 options to invest, but he can invest in only one option at a time. He
can invest either in a departmental stores, a cold storage or in an maintenance shop.
If he invests in a departmental store and succeeds he can invest in the cold storage
and if he succeeds he can invest in the car maintenance shop. If he invests in the cold
storage and succeeds he can invest in the car maintenance shop and if he succeeds he
can invest in the departmental store.
If he invests in the car maintenance shop succeeds he can invest in the cold storage
and if he succeeds he can invest in the departmental stores. Based on the data given
below, draw a decision tree and advice the investor on the best decision to take.[Jan 06]
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
INCOME Types of Milk Preferred
Low Fat Medium Fat High Fat
Low 100 225 25
Medium 125 75 150
High 75 150 275
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 14/16
Probability of
success
Investment Loss on failure
Departmental
Store
0.65 8,00,000 45,000
Cold storage 0.60 7,50,000 40,000
Maintenance shop 0.70 7,40,000 3,50,000
11.A manufacturer is faced with 2 alternatives about his products: [Jan 08]
a) Modify then existing product
b) Produce and market a new product
The first stage choice leads to further chooses only when the demand turns out to be
low. Details of this second stage are:
I stage Choice II stage
Alternative
Final Demand Probability Pay off in
LakhsA Reduce price Low 0.3 0.4
High 0.7 1.7
Increase price Low 0.8 0.6
High 0.2 2.25
B Reduce Price Low 0.2 0.5
High 0.8 1.25
Increase Price Low 1.0 0.8
High 0 2.0
Construct a decision tree and pay of table and advice the manufacturer on the best
course of action.
12.A businessman makes two independent investments A and B available to him but he
lacks the capital to undertake both of them simultaneously. He can choose to take A
first and then stop or if A is successful then take B or vice versa. The probability of
success on A is 0.7, while for B it is 0.4. Both investments require an initial capital
outlay of Rs 20,000 and both return nothing if the venture is unsuccessful. Sucessful
completion of A will return Rs 30,000 (over cost) whereas successful completion of
B will return Rs 50,000 (over cost). Draw the decision tree and determine the best
strategy. [Jan 09]
13. A restaurateur has 3 projects in hand. He can only take up one project at a time. The
first project is to take up a fast food corner at an investment of Rs 6,00,000 where the
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
Alternative Initial Demand
Probability Pay off on
High Low High
A 0.6 0.4 5 lakhs
B 0.5 0.5 7 lakhs
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 15/16
chances of success will be 0.75 with cash inflow of Rs 9,00,000. Failure means cash
inflow of Rs 1,50,000 in salvage furniture and utensils.
The second project is to open expresso coffee shop with an investment of Rs 8,00,000
where there will be definite success with an inflow of Rs 9,00,000.
The third project is to start a Darshini with an investment of Rs 10,00,000. The chance
of success are 0.6 with an inflow of Rs 12,00,000. Failure means an inflow of Rs3,00,000 in salvage material. If there is a success the restaurateur will decide to start a
fast food kiosk with an investment of Rs 4,00,000 whereby he can expect high
demand with 0.8 probability and Rs 5,00,000 inflow, medium demand with 0.15
probability and cash flow Rs 4,00,000, low demand with a cash inflow of Rs 1,00,000
All the amounts have been adjusted to current value. You are expected to draw a
decision and a payoff table and thereby advise the restaurateur about the best course
of action [Jan 10]
14. Construct index numbers of price from the following data by applying
a. Laspeyre’s b. Paasche’s c. Bowleye’s d. Marshal Edgeworth’s Method [Jan 08]
Also find the Fisher’s price index and test it for the factor reversal and time reversal
tests
Commodity Po Qo P1 Q1
A 12 18 14 16
B 15 20 16 15
C 14 24 15 20
D 13 29 12 23
E 11 28 13 21
15. The total cost of production of a firm is given by the following functions
C = 200135 + x . Find [Mar-03]
a) The total cost for an output of 65 units.
b) The average cost for an output of 100 unis
c) The marginal cost for an output of 50 units
d) If the quantity sold is 150 units, at what price should the firm sell so as to break-
even.
14. The market supply function of a commodity is q = 80 + 4P where q denotes the
quantity supplied and P denotes the market price. The unit production cost is Rs 1.50.
The government feels that a total profit of Rs 240 is desirable. What is the price that
the farmer has to receive so that he can realise this profit. [Mar 07]
15. The total cost of production of a firm is given by the following functionsC = 0.8X +14. Find [Sept-03]
a) Total cost an output of 10 units
b) The average cost of an output of 8 units
c) The marginal cost for an output of 6 units
d) If the quantity sold is 14 units at what price should the firm sell so as to breakeven?
16. The total cost of production of a firm is given by the function C= 12x2-6x+4
a) The total cost for an output of 15 units
b) The average cost for an output of 12 units
c) The marginal cost for an output of 16 units
d) The profit function for x units and price per unit of Rs 4
e) The profit for 24 units as per the profit function. [Mar-04]
17. The total cost of production of a firm is given by the function C= 10x2-5x+3
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE
5/12/2018 Bumastics_QP_final1 - slidepdf.com
http://slidepdf.com/reader/full/bumasticsqpfinal1 16/16
a) The total cost for an output of 8 units
b) The average cost for an output of 20 units
c) The marginal cost for an output of 12 units
d) The profit function for x units and price per unit of Rs 6
e) The profit for 25 units as per the profit function. [Jan05]
18. The cost function is given as C= 6 x3 + 4x2 +2. Find is x = Rs 8a) The average cost function and the average cost
b) The marginal cost function and the marginal cost
c) The revenue function if the price per unit is Rs 250 and the revenue
d) The profit function and the profit. [Jan06]
19. A firm produces a single product and it can market as many units as possible to
produce as many as 5000 units a day. The total fixed cost is Rs 2,000 daily. Unit
variable cost is Rs 0.50. How many units per day must be produced in order that the
firm breaks even [Jan 06]
20. If the cost curve C = 8 x3 + 6x2 + 3x find
a) the average cost b) the marginal cost if the quantity produced is 300 units. If the
price per unit for sales is as 2750, what is the profit or loss in the sale? [Jan 10] 21. City residents were surveyed recently to determine the readership of newspapers
available 50% of the residents read the morning newspaper 60% read the evening
newspaper and 20% read both newspapers. Find the probability that a resident
selected reads either the morning or evening paper. [Jan 07]
22. Following are the marks obtained by two students “A” and “B” in 10 tests of 100
marks each.
Tests 1 2 3 4 5 6 7 8 9 10
A 44 80 76 48 52 72 72 51 60 54
B 48 75 54 60 63 69 72 51 57 66
Find who is better in studies and if consistency is the criterion for awarding a prize,who should get the prize?
BUMASTICS [Revision paper] – RAVINDRA BABU. S[RB]-SRN ADARSH COLLEGE