Quantitative Techniques For Business Desicions

 

 

1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

End Semester Examinations – OCTOBER 2014

m.com – i semester

QUANTITATIVE TECHNIQUES FOR BUSINESS DESICIONS

Duration: 3 Hrs                                                                                           Max. Marks: 100

 

Section – A

1. Answer any SEVEN  Each carries 5 marks.                    (7 x 5  = 35)

 

1. The average number of depositors in a Post Office Savings Bank Account for the year 2008, 2009, 2010, 2011 was 2506. The number of depositors in the year 2013 was 11% higher than those in the year 2012, while the average for the six years from 2008 to 2013 was 3007. Find the number of depositors in the year 2012 and 2013.
2. Skewness measures the extent of symmetry in a distribution and Kurtosis measures the peakedness of a normal curve. Elaborate with appropriate figures.
3. The profit of a trader increases in the ratio 4:5 for the first five years but from the 6^th year his profit declines in the ratio 4:3 in the three subsequent years. His profit in the first year was 2,40,000. Find the increase in profit at the end of 8^th year as compared to first year.
4. A leading publishing house finds that the production cost directly attributed to each book is Rs.40 and the fixed cost is Rs.80,000. Assuming the cost function to be linear, find the cost function. The books can be sold for Rs.60. Find the revenue function. What is the break even point?
5. What is the probability that a non-leap year should contain 53 Sundays?
6. Calculate the Coefficient of correlation using concurrent deviation method    from the following data and interpret the result.

X	360	364	372	382	366	370	378	392	386
Y	492	480	460	434	466	454	430	390	400

 

7. With the help of following data prove that Fisher’s index number satisfies both Time reversal and Factor reversal test.

Commodity	Base Year		Current Year
	Price	Quantity	Price	Quantity
A	5	10	6	12
B	7	12	10	8
C	10	8	12	8
D	4	5	5	6
E	8	7	8	8

 

8. Given below are the figures of production (tonnes) of a sugar factory. Fit a straight line trend by the method of least squares. What is the yearly increase in the production of sugar?

Year	2005	2006	2007	2008	2009	2010	2011
Production (tones)	77	88	94	85	91	98	90

 

9. “Decision criteria under situation of uncertainty is governed by the attitude of the decision maker”. Explain

 

10. A person wants to invest in one of the three alternative investment plans: Stocks, Bonds, Savings account. It is assumed that the person wishes to invest all of the funds in a plan. The conditional payoffs of the investments are based on three potential economic conditions: accelerated, normal or slow growth. The payoff matrix is given below. What will be the person’s decision if he uses the following criterion. i)Maxi-Max Criterion ii)Maxi-Min Criterion iii) Mini-Max Regret Criterion   iv)Laplace Criterion

 

Events Economic Conditions	Acts Alternative investments
	Stocks	Bonds	Savings Account
Accelerated Growth	10000	8000	5000
Normal Growth	6500	6000	5000
Slow Growth	-4000	1000	5000

 

 

                                                   Section – B

1. Answer any THREE Each carries 15 marks.                       (3 x 15   = 45)

11)  Total cost of production of a firm is given by  C= 300x -10x²+ (x³/3) . Where C stands for cost and x for output. Calculate

1. a) Output at which marginal cost is minimum.
2. b) Cost and average cost when 50 units are manufactured.
3. c) Output at which marginal cost is equal to average cost.

(5+5+5)

12) a) From the prices X and Y of shares A and B respectively given below, find standard deviation, coefficient of variation and state which share is more stable in value?

 

Price of Share A (X) :	55	54	52	53	56	58	52	50	51	49
Price of Share B (Y):	108	107	105	105	106	107	104	103	104	101

 

 

 

 

 

 

1. b) Find the missing information in the following table:

 

	Groups			Combined
	A	B	C
Number of values	10	8	–	24
Mean	20	–	6	15

(10 + 5)

 

13) a) An office has 4 secretaries handling respectively 20%, 60%, 15% and 5% of the files of all government reports. The probability that they misfile such reports are respectively 0.05, 0.1, 0.1 and 0.05.  Using Baye’s theorem find the probability that the misfiled report can be blamed on the first secretary.

1. b) In class there are 5 students who often come late. A teacher has studied the situation over a period of time and determined that there is a 0.4 chance of any one student being late. They arrive independently of each other. Using binomial distribution find the probability of three or more students coming late to class.
2. c) In a test on electric bulbs it was found that the lifetime of a particular brand was distributed normally with an average life of 2000 hrs and standard deviation of 60 hrs. If a firm purchases 2500 bulbs find the number of bulbs that are likely to last between 1900 and 2050 hrs.

(5+5+5)

 

14) Calculate Karl Pearson’s coefficient of correlation between advertising expenditure and sales from the data given below. It is observed that advertising expenditure incurred has impact on sales  after two months. Find probable error. Is coefficient of correlation significant?

Advertising

Expenditure

(‘000 Rs.)             39    65    62    90    82    75    25    98    36    78

_________________________________________________________

Sales

(Lakh Rs.)            47    53    58    86    62    68    60    91    51    84

 

15)  A group of students raise money each year by selling souvenirs outside the stadium after a cricket match between team A and B. Their sales are mostly dependent on which team wins the match. A conditional pay off table is given as under. If the probability of Team A winning is 0.6, Calculate  i)EVM   ii) EOL  iii) EPPI  iv) EVPI.  Which type of souvenir should the students buy?  Convert the pay off table into a decision tree and identify the best decision.

 

 

Events	Acts Type Of Souvenir
	I	II	III
Team A wins	Rs.1200	Rs.800	Rs.300
Team B wins	Rs.250	Rs.700	Rs.1100

 

 

Section – C

 

• Compulsory Case study.                                                                             (1 x 20 = 20)

 

16. The following table shows a portion of the human resource data on a client company.

 

Client company human resource data by gender

Type of position	Gender
	Male	Female
Managerial	8	3
Professional	31	13
Technical	52	17
Clerical	9	22
Total	100	55

 

1. i) If a worker is randomly selected from the client company what is the probability that the worker is a woman?
2. Suppose a special bonus is being given to one person in the technical area, if the bonus is randomly awarded what is the probability that it will go to a man?

• If a worker is randomly selected what is the probability that the worker is either technical or clerical.

Suppose at the annual holiday party an employee will be randomly drawn to win a trip to Hawaii, what is the probability that:

1. a professional person will be a winner.
2. The winner will be either a man or a clerical worker?
3. The winner is a woman and in management?

• Suppose the winner is a man, what is the probability that he is from the technical group?

 

1. “Karl Pearson’s measure of skewness of a distribution is 0.5. Its median and mode are respectively 42 and 36.  Find Mean, Standard deviation, Variance & Coefficient of variation.                                                                                                                  (14 +6)