M.B.A-M.B.A 1st Sem 104 : Statistical and Quantitative Methods(University of Pune, Pune-2013)

Total No. of Questions : 6]                      [Total No. of Pages : 3

                  [4375] - 104

                    M.B.A. (Semester - I)

            104 : Statistical and Quantitative Methods

                               (2008 Pattern)

Time :3 Hours]                                                                                                 [Max. Marks :70

Instructions to the candidates:-

1) Solve any two questions from section I, and any two questions from section II.

2) Use of electronic calculator and statistical tables are allowed.

3) Graph paper will not be provided, draw all graphs and sketches on answer

paper.

SECTION - I

Q1) a)      From the following table showing age of cars of a certain make and

annual maintenance costs obtain the regression equation for the cost related to age. Estimate the approximate cost of maintaining a 3 year old

car.                                                                                                                        [9]

Age of car (yrs)      2           4           6            7            8             10           12

Maint cost Rs.     4800      4500    5400      5700       6000         6500       8000

b)       In a sample survey of 2500 students 1000 liked Economics, 1750 liked

statistics and 600 liked both. Find whether liking in two subjects is

associated or not?                                                                                          [8]

Q2) a)      Calculate mean, median and mode for the following data.              [9]

Class limits             30-59 60-89 90-119 120-149 150-179 180-209

Frequency                  10           25           35             20               10              7

b)       Calculate coefficient of variation and compare                                    [8]

x            35          38          37         40           32

y          126     130    100    120      125

Q3) a)      Tickets numbered from 1 to 100 are shuffled and a ticket is drawn. What

is the probability that the drawn ticket has                                          [6]

i) an odd number

ii) A number 5 or its multiple

P.T.O.

b)       An experiment succeeds twice as many times as it fails. Find the chance

that in six trials there will be at least one success?                            [6]

c)       An insurance company receives on an average 2 telephone calls every 15

minutes. Find the probability that no call be received in 30 minute interval

(Given e–4 = 0.01832, e–2 = 0.113534                                                      [5]

SECTION - II

Q4) a)      There are three factories and four warehouses. Unit transportation cost

matrix is given as below capacities at factories and demand at warehouses

is also given. Find optimum solution.                                                     [9]

Factory                        Warehouse                  Capacity

W1  W2  W3   W4                    (units)

F1                     10   30   50    10                         7

F2                     70   30   40    60                         9

F3                     40    8     70    20                        18

Demand                 5       8       7       15

(units)

b)       The following data gives cost incurred if a job is performed on different

machines. Their are 4 jobs and 4 machines. Assign jobs to machines so

that total cost is minimum.                                                                         [9]

Jobs

Machines            A      B     C            D

M1                  3       8      5            9

M2                  4       2      1            6

M3                  3       8      5            7

M4                                            4        7     10            8

Q5) a) The Agricultural Research Institute has suggested to a farmer to spread out at least 4800 kgs of a special phosphate fertilizer and no less than 7200 kgs of a special nitrogen fertilizer to raise the productivity of the crop in his fields. There are two sources of obtaining these mixtures. Mixture A and mixture B both are available in bags weighting 100 kg each and they cost Rs. 40 and Rs. 24 respectively. Mixture A contains phosphate and nitrogen equivalent of 20kg and 80kg respectively. While mixture B contains these ingredients equivalent of 50kgs each type. Determine how many bags of each type should the farmer buy in order to obtain the required at minimum cost.                                                [9]

[4375]-104                                                     2

b)       In a management institute the first lecture starts at 9 A.M. following is the

probability distribution regarding late comers for the first lecture day.[9]

Late by minutes             2           4            6           8         10        12

Probability                   0.40        0.30       0.20      0.05   0.03   0.02

Simulate the system for 10 students and find percentage of students late by more than 6 minutes.

Use following random numbers.

99, 89, 10, 27, 50, 93, 92, 57, 50, 78

Q6) a)      Solve the following Game                                                                                  [6]

B1      B2

A1     6       -3

A2     -3     0

b)       Given the following pay off matrix use Herwicz criterion and find which

action to be taken (Given = 0.7)                                                           [6]

States of nature                Actions

A1      A2   A3       A4

S1                         10        5       8         6

S2                           3       9      15         2

S3                          -3       4       6        10

c)       In a bank on an average every 15 minutes one customer arrives for cashing

the cheque. The staff at the only payment counter takes 10 minutes for

serving a customer on an average.                                                           [6]

Find

i)  The average queue length

ii)  Increase in arrival rate for justifying a second counter (When the waiting time of a customer is at least 15 minutes, the management will increase one more counter).

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