Download GTU (Gujarat Technological University) MBA (Master of Business Administration) 2019 Summer 1st Sem 3519207 Business Statistics Previous Question Paper

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA SEMESTER I? ? EXAMINATION ? SUMMER-2019

Subject Code: 3519207 Date: 22/05/2019

Subject Name: Business Statistics

Time: 02:30 PM To 05:30 PM Total Marks: 70

Instructions:

1. Use of statistical table is allowed.

2. Figures to the right indicate full marks.

Q ? 1

Briefly discuss the following concepts:

a) Index numbers

b) Autocorrelation

c) Cumulative frequency

d) Characteristics of normal distribution

e) Coefficient of determination

f) Posterior probability

g) Explain Chebyshev?s theorem

14

Q ? 2 (A) There are two clubs in a society. In this, 60% members of the society are members of

club A and 29% members of the society are member of club B. Whereas 13%

members of the society are member of both clubs. Suppose one member is selected

randomly,

1) What is the probability that he is a member of club A or club B?

2) What is the probability that he is neither member of club A nor club B?

3) What is the probability that he is not a member of club A but member of club B?

7

Q ? 2 (B) In MBA semester I, unit test of 100 marks was administered for 100 students. The

result is as under:

Marks Number of Students

Below 10 4

Below 20 6

Below 30 24

Below 40 46

Below 50 67

Below 60 86

Below 70 96

Below 80 99

Below 90 100

Based on this information, develop the frequency distribution table and calculate

mean, median and mode of the data.

7

OR

Q ? 2 (B) Discuss nominal, ordinal, interval and ration data types with examples.

7

Q ? 3 (A) Workers in the manufacturing sector are subject to work related injuries. The

Government labour department estimates that the average cost of these injuries to

7

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Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA SEMESTER I? ? EXAMINATION ? SUMMER-2019

Subject Code: 3519207 Date: 22/05/2019

Subject Name: Business Statistics

Time: 02:30 PM To 05:30 PM Total Marks: 70

Instructions:

1. Use of statistical table is allowed.

2. Figures to the right indicate full marks.

Q ? 1

Briefly discuss the following concepts:

a) Index numbers

b) Autocorrelation

c) Cumulative frequency

d) Characteristics of normal distribution

e) Coefficient of determination

f) Posterior probability

g) Explain Chebyshev?s theorem

14

Q ? 2 (A) There are two clubs in a society. In this, 60% members of the society are members of

club A and 29% members of the society are member of club B. Whereas 13%

members of the society are member of both clubs. Suppose one member is selected

randomly,

1) What is the probability that he is a member of club A or club B?

2) What is the probability that he is neither member of club A nor club B?

3) What is the probability that he is not a member of club A but member of club B?

7

Q ? 2 (B) In MBA semester I, unit test of 100 marks was administered for 100 students. The

result is as under:

Marks Number of Students

Below 10 4

Below 20 6

Below 30 24

Below 40 46

Below 50 67

Below 60 86

Below 70 96

Below 80 99

Below 90 100

Based on this information, develop the frequency distribution table and calculate

mean, median and mode of the data.

7

OR

Q ? 2 (B) Discuss nominal, ordinal, interval and ration data types with examples.

7

Q ? 3 (A) Workers in the manufacturing sector are subject to work related injuries. The

Government labour department estimates that the average cost of these injuries to

7

2

employers and insurers is approximately Rs. 30000 per injured worker. Suppose these

costs are normally distributed with a standard deviation of Rs. 9000/-.

1) What proportions of the costs are between Rs. 15000 to Rs. 45000?

2) What proportions of the costs are greater than Rs. 50000?

3) What proportions of the costs are between Rs. 5000 and Rs. 20000?

4) Suppose the standard deviation is unknown, but 90.82%of the costs are more

than Rs. 7000, what would be the value of standard deviation?

Q ? 3 (B) A survey showed that the average number of annual trips per family in Gujarat is

Poisson distributed, with a mean of 0.7 trips per year. A family is selected randomly.

What is the probability that

1) The family didn?t make a trip last year?

2) The family took two or more trips last year?

3) The family took tree or fewer trips over five-year period?

4) The family took exactly 4 trips during a six-year period?

7

OR

Q ? 3 (A) Briefly discuss Binomial distribution and Poisson distribution. What are the

conditions in which Poisson distribution is used as an approximation of Binomial

distribution?.

7

Q ? 3 (B) Mr. Patel, a farmer has collected the following information describing the prices and

quantities of three harvested crops for the year 2011 ? 2014:

Price (in Rs. Per ton) Quantity Harvested (tons)

Type of

Crop ?

2011 2012 2013 2014 2011 2012 2013 2014

X 108 109 113 111 1280 1150 1330 1360

Y 93 96 96 101 830 860 850 890

Z 97 99 106 107 1640 1760 1630 1660

Construct a Laspeyres price index for each of these four years using 2011 as the base

year.

7

Q ? 4 (A) Depict your understanding for Time-Series Analysis. Also discuss the components of

Time-Series.

7

Q ? 4 (B) Generally, accountants estimate overhead based on the level of production. At

Shriram co., they have collected information on overhead expenses and units

produced at different plants as under:

Overhead 191 170 272 155 280 173 234 116 153 178

Units 40 42 53 35 56 39 48 30 37 40

1) Develop the regression equation for accountants.

2) Predict overhead when 50 units are produced.

3) Calculate the standard error of estimate.

7

OR

Q ? 4 (A) Explain simple and multiple regression with suitable examples.

7

Q ? 4 (B) Depict your understanding for correlation and types of correlation. What is the use of

Coefficient of correlation in statistics?

7

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1

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

MBA SEMESTER I? ? EXAMINATION ? SUMMER-2019

Subject Code: 3519207 Date: 22/05/2019

Subject Name: Business Statistics

Time: 02:30 PM To 05:30 PM Total Marks: 70

Instructions:

1. Use of statistical table is allowed.

2. Figures to the right indicate full marks.

Q ? 1

Briefly discuss the following concepts:

a) Index numbers

b) Autocorrelation

c) Cumulative frequency

d) Characteristics of normal distribution

e) Coefficient of determination

f) Posterior probability

g) Explain Chebyshev?s theorem

14

Q ? 2 (A) There are two clubs in a society. In this, 60% members of the society are members of

club A and 29% members of the society are member of club B. Whereas 13%

members of the society are member of both clubs. Suppose one member is selected

randomly,

1) What is the probability that he is a member of club A or club B?

2) What is the probability that he is neither member of club A nor club B?

3) What is the probability that he is not a member of club A but member of club B?

7

Q ? 2 (B) In MBA semester I, unit test of 100 marks was administered for 100 students. The

result is as under:

Marks Number of Students

Below 10 4

Below 20 6

Below 30 24

Below 40 46

Below 50 67

Below 60 86

Below 70 96

Below 80 99

Below 90 100

Based on this information, develop the frequency distribution table and calculate

mean, median and mode of the data.

7

OR

Q ? 2 (B) Discuss nominal, ordinal, interval and ration data types with examples.

7

Q ? 3 (A) Workers in the manufacturing sector are subject to work related injuries. The

Government labour department estimates that the average cost of these injuries to

7

2

employers and insurers is approximately Rs. 30000 per injured worker. Suppose these

costs are normally distributed with a standard deviation of Rs. 9000/-.

1) What proportions of the costs are between Rs. 15000 to Rs. 45000?

2) What proportions of the costs are greater than Rs. 50000?

3) What proportions of the costs are between Rs. 5000 and Rs. 20000?

4) Suppose the standard deviation is unknown, but 90.82%of the costs are more

than Rs. 7000, what would be the value of standard deviation?

Q ? 3 (B) A survey showed that the average number of annual trips per family in Gujarat is

Poisson distributed, with a mean of 0.7 trips per year. A family is selected randomly.

What is the probability that

1) The family didn?t make a trip last year?

2) The family took two or more trips last year?

3) The family took tree or fewer trips over five-year period?

4) The family took exactly 4 trips during a six-year period?

7

OR

Q ? 3 (A) Briefly discuss Binomial distribution and Poisson distribution. What are the

conditions in which Poisson distribution is used as an approximation of Binomial

distribution?.

7

Q ? 3 (B) Mr. Patel, a farmer has collected the following information describing the prices and

quantities of three harvested crops for the year 2011 ? 2014:

Price (in Rs. Per ton) Quantity Harvested (tons)

Type of

Crop ?

2011 2012 2013 2014 2011 2012 2013 2014

X 108 109 113 111 1280 1150 1330 1360

Y 93 96 96 101 830 860 850 890

Z 97 99 106 107 1640 1760 1630 1660

Construct a Laspeyres price index for each of these four years using 2011 as the base

year.

7

Q ? 4 (A) Depict your understanding for Time-Series Analysis. Also discuss the components of

Time-Series.

7

Q ? 4 (B) Generally, accountants estimate overhead based on the level of production. At

Shriram co., they have collected information on overhead expenses and units

produced at different plants as under:

Overhead 191 170 272 155 280 173 234 116 153 178

Units 40 42 53 35 56 39 48 30 37 40

1) Develop the regression equation for accountants.

2) Predict overhead when 50 units are produced.

3) Calculate the standard error of estimate.

7

OR

Q ? 4 (A) Explain simple and multiple regression with suitable examples.

7

Q ? 4 (B) Depict your understanding for correlation and types of correlation. What is the use of

Coefficient of correlation in statistics?

7

3

Q ? 5 A manufacturing company has installed a machine costing Rs. 4 lacs and is in the

process of deciding on an appropriate number of certain spare parts required for

repairs. The spare parts cost Rs. 4000 per unit but are available only if they are

ordered now. In case the machine fails and no spares are available, the cost to the

company of mending the plant would be Rs. 18000/-. The plant has an estimated life

of 8 years and the probability distribution of failure during this time, based on

experience with similar machines, is as under:

No. of failures during

8-yearly period

0 1 2 3 4 5 6+

Probability 0.1 0.2 0.3 0.2 0.1 0.1 00

Ignoring any discounting for time value of money, determine the following:

a) The optimal number of units of the spare part on the basis of minimax

principle, minimin principle, Laplace principle, and Hurwicz Principle (by

Taking ? =0.7).

b) The expected number of failures in the 8-year period.

OR

a) The optimal choice on the basis of least expected regret criterion using the

regret table.

b) Expected Value of Perfect Information.

14

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This post was last modified on 19 February 2020