St. Joseph’s College of Commerce 2015 Mathematics & Statistics For Managers Question Paper PDF Download

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St. Joseph’s College of Commerce (Autonomous)
END SEMESTER EXAMINATION – SEPT/OCT. 2015
M.COM (I.B.) – I SEMESTER
P415 AR 101: MATHEMATICS & STATISTICS FOR MANAGERS
Duration: 3 Hours                                                                                                     Max. Marks: 100
Note: Students can use any scientific calculator. Workings should be part of your answers.
SECTION – A
I. Answer any SEVEN questions.  Each carries 5 marks.                                   (7×5=35)
  1. Consider the decision of whether to reopen Kolar Gold mine. The cost of doing so is expected to be Rs. 1,00,00,000.  It is estimated 40,000 ounces of gold remaining in the mine. It can be extracted with in a year and make a profit of Rs.1000 per ounce of gold if gold price reaches to Rs.30,000.  If the price is below Rs.30,000 it is not viable. The probability of  price being Rs. 30,000 is 0.3. Calculate the expected profit or loss.
  2. For the following numbers, calculate: 2,1,2,3,1,3,3,4,3,5 and 6.

a)      Mean  b) Median  c) Mode
  3. 1.      The number of accidents in a year attributed to taxi-drivers in a city follows Poisson distribution with mean 2.5. Out of 1,000 taxi drivers, find the number of drivers with no accident in a year.
  4. Calculate Fisher’s index and the % of inflation from the following information.

Base Year Current year
Price Quantity Price Quantity
30

50

25

20

 5

7

3

3

 

 35

52

30

18

 6

8

3

4
  5. 2.      The regression coefficients are: bxy = – 0.8 and byx = – 0.7. Calculate the following: a) Correlation Coefficient b) Variation due to other reasons (residuals)(Coefficient of non-determination).
  6. An apartment complex has 400 apartments to rent. If they rent x apartments then their monthly profit, in rupees, is given by, P(x) = – 8x² + 4800x – 80,000. How many apartments should they rent in order to maximize their profit?
  7. There are two boxes. First box contains 3 Red, 4 White and 6 Black coins. The second box contains 4 Red, 3 White and 5 Black coins. One coin is drawn each box simultaneously. Find the probability that:

a)      Both the coins are red

b)     One coin is Black and another is White.

c)      Neither of them are red and white.
  8.  Vehicles pass through a junction on a busy road at an average rate of 300 per hour.

i)       Find the probability that none passes in a given minute.

ii)           ii) What is the expected number passing in two minutes?
  9.
  Coefficients
Intercept 3.910934467
X Variable 1 -0.09064735
X Variable 2 -0.00614618
X Variable 3 0.000449966

Form a regression equation from the above information and give a brief note on each value given above.
  10. There is a political uncertainty  prevailing in Syria where current project of an Indian company under operation. There are two options available.

i)                   Close down the company and bring  to India with in a month $ 1,00,000 ( 1$ = Rs. 66.67.

ii)                 If the company is not closed down now it can close down after six months then, the  Syrian Government may restrict the Indian company not to take more than 60% of sale value of $ 60,000 after six months (Expected currency value is 1$ = Rs.69. The probability of  closing down now is 0.80 and the probability of closing down after 6 months is 0.20.

Calculate the expected value and standard deviation.
 

SECTION – B
II. Answer any THREE questions.  Each carries 15 marks.                                              (3×15=45)
  11. i)                   The following table gives monthly wages of workers in a factory:

Monthly wages in Rupees ‘000 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90
No. of workers 5 20 10 10 9 6 12 8

Calculate:

a)      The mean

b)     The modal class

c)      The number of workers getting monthly wages below Rs.80,000

d)     The number of workers getting Rs.65,000 or more, but less than Rs. 85,000 as monthly wages.

(ii) Find the probability of having 53 Sundays in:

a)      A non- leap year

b)     A leap year
  12. a)      Offices in a college are open for 5 days in a week(Monday to Friday). Two employees of an office remain absent for one day in  the same week. Find the probability that they remain absent on: a) The same day  b) Consecutive day  c) Different days

b)     A box contains some black balls and 30 white balls. If the probability of drawing a black ball is 2/5th  of a white ball; find the number of black balls in the box.
  13. 3.      a) The revival of the M’s Indian economy depends on increase in the world crude oil production and the fall of South East Asian economy excluding India. The probability  of increase in oil production is 0.6 and the probability of the fall of the South East Asian Economy excluding India is 0.3. What is the probability of the revival of  M’s Indian  economy?

b) The electronic fly over is currently charging Rs.40 one way per day. The average number of cars travelling per day is 25,000. The contractor concludes that by increasing toll from Rs.40 to Rs.50 the reduction in number of cars is 800. What toll has to be charged to maximize the revenue?
  14. Explain/fill in / calculate  any ten of the following:

a)      R^2= 0.70(Explain)

b)     P=0.40; q =?

c)      Relationship between Slope and differential calculus.

d)     In a second derivative the value becomes negative why do we say it is the maximum value?

e)      If Mean=Median = Mode the distribution is ____________.

f)       Binomial distribution can be used only when there are ___________ possible events .

g)     When n tends to infinitive and p tends to zero we use ______________ distribution.

h)     Correlation range is between______________ to _______________.

i)       Probability range is between _________________ to _______________.

j)        Write down the characteristics of an  independent and a dependent variable.

k)     What do you understand from co-efficient of non-determination?

l)       The ideal Index has to fulfill __________ and ___________ tests.

 
  15. Calculate correlation coefficient between two markets’ share prices prevailing over 7 days from the following data:

Days           :  1    2      3     4     5     6      7

Market A   : 20   22   22   24   26   26    25

Market B   : 20   19    20   21   25   24   24
 

 

 

 

 

 

 

 

SECTION – C
III. Case Study                                                                                                                      (1×20=20)
  16. PRICES OF THE INGREDINTS SPECIFIED IN TEH 15TH ILC TO CALCULATE THE MINIMUM WAGES AS ON 01.05.2014 in Indian cities.

ITEMS D
E
L
H
I		 M
U
M
B
A
I		 K
O
L
K
T
A		 C
H
E
N
N
A
I		 B
A
N
G
A
L
O
R
E		 B
H
U
B
A
N
E
S
H
W
A
R		 T
R
I
V
A
N
D
R
U
M		 H
Y
D
E
R
A
B
A
D		 A
V
E
R
A
G
E

A

M

0

U

N

T

 PCU
/day
in
gms		 Per
Month
3
CU
(inKg)		 Total amount per month
Rice/Wheat 44 49 44 48 47 58 42 44 47 475 gms 42.75 kg 2009
Dal (Toor/Urid/Moong) 99 102 140 100 97 97 95 94 103 80 gms 7.2 kg 742
Raw Vegetables 44 46 41 40 42 50 48 41 44 100 gms 9.00 kg 396
Green Vegetables 42 43 40 42 42 43 44 40 42 125 gms 11.25 kg 473
Other Vegetables 43 43 41 40 40 41 49 40 41 75 gms 6.75 kg 277
Fruits 111 114 108 112 109 108 108 109 110 120 gms 10.8 kg 1188
Milk 44 44 39 39 36 36 36 38 39 200 ml 18 ltr 702
Sugar/Jaggery 44 43 42 44 45 44 46 44 44 56 gms 5.00 kg 220
Edible Oil 148 159 142 159 142 141 141 140 138 40 gms 3.6 kg 497
Fish 315 325 315 375 305 310 335 320 325 2.5 kg 813
Meat 423 420 438 388 403 397 398 488 425 5.0 kg 2125
Egg 5 5 5 5 5 5 5 5 5 90 Nos 450
Detergents 404 414 379 399 379 399 399 399 396 396
Clothes 198 203 178 198 178 198 198 188 192 5.5 mtr 1056
Total 11344
Housing @ 7.5% 1174
Miscellaneous @20% 3129
Total 15647
Additional @ 25% 5214
Grand Total – Minimum pay for unskilled worker in the erstwhile Group D 20861
Minimum pay for Group C added with 25% with the minimum of above 5214
Minimum Pay at Group C level 26075
Rounded off to 26000

 

 

The 7th CPC also would adopt Dr. Aykroyd formula for the computation of the minimum wage and thereafter the fitment formula is calculated.

Fitment formula = Minimum wage / Rs 7000

The Staff Side (JCM) has calculated the fitment formula of 3.72 that is Rs 26000/ Rs 7000 as on 1st Jan 2014.

The 7th CPC has hinted that the date of effect of the 7th CPC shall be from 1st Jan 2016. In this context the minimum wage and fitment formula, should be as follows.

The increase in prices between 1st Jan 2014 to 1st July 2015 is 18% as the DA as on 1st Jan 2014 was 100% and likely DA as on 1st July 2015 is 118%, In actual terms the retail prices have increased by over 25%. Even considering the 18% hike in prices from 1st Jan 2014 to 1st July 2015 and adding 7 % likely hike in prices for the period 1st July 2015 to Jan 2016 it works out to 25% hike in minimum wage.

Minimum wage calculated by the Staff Side (JCM) using Dr. Aykroyd formula as on 1st Jan 2014 was Rs 26,000/-

Required:

a)     Calculate pay package for the cities  Bangalore, Chennai and Trivandram based on the method followed above for the country and fitment formula.

b)     As per 6th pay commission the minimum pay was Rs. 7000 as on  1/1/2006. Keeping 1/1/2006 as a base, calculate index for the cities each Bangalore and Trivandram.

 

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