Page 1 of 3

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER 01? ? EXAMINATION ? SUMMER-2018

Subject Code: 3519207 Date:04/05/2018
Time: 10:30AM To 1:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 Explain following terms
1. coefficient of variation
2. marginal probability
3. multicollinearity
4. autocorrelation
5. family budget and cost of living index
6. cyclical variations
7. Random experiment

14
Q.2 A. Find mean, median and mode for following data

Age Frequency
15-20 9
20-25 16
25-30 27
30-35 44
35-40 42
40-45 23
45-50 7
50-55 2

07
B. Write a note on decision theory 07
OR
B. Write a note on statistical graphs and charts 07
Q.3 A Assume that a factory has two machines. Past records show that machine 1
produces 30 % of the items of output and machine 2 produces 70 percent of
items. Further 5 % of the items produced by machine 1 were defective and
only 1 % produced by machine 2 were defective. If a defective item is drawn
at random what is the probability that the defective item was produced by
machine 1 or machine 2?
07
B 1. 15
C
5
2. 15
P
5
07
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Page 1 of 3

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER 01? ? EXAMINATION ? SUMMER-2018

Subject Code: 3519207 Date:04/05/2018
Time: 10:30AM To 1:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 Explain following terms
1. coefficient of variation
2. marginal probability
3. multicollinearity
4. autocorrelation
5. family budget and cost of living index
6. cyclical variations
7. Random experiment

14
Q.2 A. Find mean, median and mode for following data

Age Frequency
15-20 9
20-25 16
25-30 27
30-35 44
35-40 42
40-45 23
45-50 7
50-55 2

07
B. Write a note on decision theory 07
OR
B. Write a note on statistical graphs and charts 07
Q.3 A Assume that a factory has two machines. Past records show that machine 1
produces 30 % of the items of output and machine 2 produces 70 percent of
items. Further 5 % of the items produced by machine 1 were defective and
only 1 % produced by machine 2 were defective. If a defective item is drawn
at random what is the probability that the defective item was produced by
machine 1 or machine 2?
07
B 1. 15
C
5
2. 15
P
5
07
Page 2 of 3

OR
Q.3 A For given data construct laspeyre quantity index and paasche quantity index.
(base year 1998)

item Quantity in
1998
Quantity in
2005
Price per unit
in 1998
Price per unit
in 2005
1 4 8 100 150
2 5 12 55 110
3 6 8 75 145
4 5 8 85 165
5 8 15 75 155

07

B

A service station has a pump that distributes diesel fuel to automobiles. The
station owner estimates that only about 4 cars use the diesel pump every two
hours. Assume the arrivals of diesel pump users are Poisson distributed.
a. what is the probability that three cars will arrive to use the diesel pump
during a 1- hour period?
b. supposes the owner needs to shut down the diesel pump for half an hour to
make repairs. However, the owner hates to lose any business. What is the
probability that no cars will arrive to use the diesel pump during a half hour
period?

07
Q.4 A Noida realty corporation has purchased land in the outskirts of greater Noida
to develop an integrated township. NRC has three alternatives, namely to
develop a township to house 10,000 families or to develop a golf course with
1000 luxury villas or to develop an integrated software complex with 6000
apartments and office space of 25000 sq. ft. The company foresees two states
of nature, namely a situation where there is a strong demand for the project or
a situation where there is a weak demand for the project. Following table
provides the details of the payoff for the various decision alternatives. There
is 65 % probability that there will be strong demand.
Construct decision tree to graphically represent the decision scenario and using
the expected value criterion. Select the alternative with the highest expected
payoff.

Decision alternative State of nature
Strong demand Weak demand
An integrated township
to house 10000 families
10 3
A golf course with 1000
luxury villas
25 3
An integrated software
complex
20 3

07
B Write a detail note on correlation and regression. Discuss difference between
simple regression and multiple regression using example.
07
OR
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Page 1 of 3

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
MBA ? SEMESTER 01? ? EXAMINATION ? SUMMER-2018

Subject Code: 3519207 Date:04/05/2018
Time: 10:30AM To 1:30 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 Explain following terms
1. coefficient of variation
2. marginal probability
3. multicollinearity
4. autocorrelation
5. family budget and cost of living index
6. cyclical variations
7. Random experiment

14
Q.2 A. Find mean, median and mode for following data

Age Frequency
15-20 9
20-25 16
25-30 27
30-35 44
35-40 42
40-45 23
45-50 7
50-55 2

07
B. Write a note on decision theory 07
OR
B. Write a note on statistical graphs and charts 07
Q.3 A Assume that a factory has two machines. Past records show that machine 1
produces 30 % of the items of output and machine 2 produces 70 percent of
items. Further 5 % of the items produced by machine 1 were defective and
only 1 % produced by machine 2 were defective. If a defective item is drawn
at random what is the probability that the defective item was produced by
machine 1 or machine 2?
07
B 1. 15
C
5
2. 15
P
5
07
Page 2 of 3

OR
Q.3 A For given data construct laspeyre quantity index and paasche quantity index.
(base year 1998)

item Quantity in
1998
Quantity in
2005
Price per unit
in 1998
Price per unit
in 2005
1 4 8 100 150
2 5 12 55 110
3 6 8 75 145
4 5 8 85 165
5 8 15 75 155

07

B

A service station has a pump that distributes diesel fuel to automobiles. The
station owner estimates that only about 4 cars use the diesel pump every two
hours. Assume the arrivals of diesel pump users are Poisson distributed.
a. what is the probability that three cars will arrive to use the diesel pump
during a 1- hour period?
b. supposes the owner needs to shut down the diesel pump for half an hour to
make repairs. However, the owner hates to lose any business. What is the
probability that no cars will arrive to use the diesel pump during a half hour
period?

07
Q.4 A Noida realty corporation has purchased land in the outskirts of greater Noida
to develop an integrated township. NRC has three alternatives, namely to
develop a township to house 10,000 families or to develop a golf course with
1000 luxury villas or to develop an integrated software complex with 6000
apartments and office space of 25000 sq. ft. The company foresees two states
of nature, namely a situation where there is a strong demand for the project or
a situation where there is a weak demand for the project. Following table
provides the details of the payoff for the various decision alternatives. There
is 65 % probability that there will be strong demand.
Construct decision tree to graphically represent the decision scenario and using
the expected value criterion. Select the alternative with the highest expected
payoff.

Decision alternative State of nature
Strong demand Weak demand
An integrated township
to house 10000 families
10 3
A golf course with 1000
luxury villas
25 3
An integrated software
complex
20 3

07
B Write a detail note on correlation and regression. Discuss difference between
simple regression and multiple regression using example.
07
OR
Page 3 of 3

Q.4 A The lifetime of certain kinds of electronic devices will have a mean of 300
hours and standard deviation of 25 hours. Assuming that the distribution of
these lifetimes, which are measured to be the nearest hours, can be
approximated closely with a normal curve,
i. What percentage will have lifetime of 350 hours or less?
ii. What percentage will have lifetimes from 220 or 260 hours?

07
B Fit the trend line and calculate trend for the year 1960.

X Y
1950 28
1951 35
1952 42
1953 10
1954 22
1955 39
1956 28

07

Q.5

Consider following observations:

123,250,352,143,112,324,256,235,412,156

14
A Prepare five point summary
B Prepare box and whisker plot

OR

A Find mean and standard deviation
B Find range, P80 and D7.

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