# Business Statistics and Operation Research in Business Question Paper’ 2021 (Held in 2022), Gauhati University

## The figures in the margin indicate full marks for the questions.Â

Answer Questions Nos. 1, 2, 3 and any four from the rest.

1. (a) Select the correct answer: 1×4=4

1. Sum of the squares of deviations of the given set of observations from their arithmetic means is

1. Maximum.Â

2. Minimum.Â

3. Zero.Â

4. None of the above.Â

1. Standard deviation is dependent on the change ofÂ

1. Origin.Â

2. Scale.Â

3. Origin and scale.Â

4. None of the above.Â

1. Seasonal variations areÂ

1. Short-term variations.Â

2. Long-term variations.Â

3. Sudden variations.Â

4. Cyclical variations.Â

1. Coefficient of variations is calculated by the formulaÂ

1. .

2. .

3. .Â

4. .

(b) Fill in the blanks: 1×3=3

1. An index number is a special type of _______.Â

2. Correlation coefficient is _______ of two regression coefficients.Â

3. If A and B are mutually exclusive events, _______.Â

(c) Write True or False: 1×2=2

1. An average alone is sufficient to understand the basic characteristics of a frequency distribution.Â

2. Mean of binomial distribution is always greater than variance.Â

(d) What do you mean by sample? 1

2. Answer the following questions: 2×5=10

1. What is estimation?

2. Write two properties of correlation coefficient.Â

3. Two regression coefficients in a distribution are calculated as â€“ 1.89 and â€“ 0.52. Is it possible? Justify your answer.Â

4. Find the E(X) for the following probability distribution of X:Â

 X: 0 1 2 3 P:
1. Define skewness.Â

3. Answer any four of the following questions: 5×4=20

1. What is sample survey? Write the advantages and disadvantages of sample survey.Â

2. Prove that the expectation of a random variable x is equal to the arithmetic mean.Â

3. Discuss briefly various problems involved in the construction of index numbers.Â

4. Given the two regression equations as follows: and . Find the correlation coefficient between x and y.Â

5. State the additive law of probability and explain it with an example.Â

6. What do you mean by correlation between two variables? Mention different types of correlation.Â

4. (a) A study of 100 companies gives the following information:Â

 ProfitÂ  (Rs. in crore): 0-10 10-20 20-30 30-40 40-50 50-60 NumberÂ  of companies: 8 12 20 30 20 10

Calculate mean and standard deviation of the profit earned. 3+3=6

(b) Mention the desirable properties of a good measure of dispersion. 4

5. (a) Find the coefficient of correlation between X and Y from the following data: 6

 X: 10 6 9 10 12 13 11 9 Y: 9 4 6 9 11 13 8 4

(b) What is a regression line? What purpose does it serve? When are the two regression lines identical?Â  Â  2+1+1=4

6. (a) What is a binomial probability distribution? Mention the properties of this distribution. 2+4=6

(b) In a business a person can make a profit of Rs. 2,00,000 with a probability of 0.4 or have a loss of Rs. 1,00,000 with a probability of 0.6. What is his expected profit? 4

7. (a) Write the probability density function of a normal distribution. Under what conditions a binomial distribution tends to a normal distribution? 3+2=5

(b) If 5% of electric bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs (1) 3 bulbs will be defective and (2) none will be defective. (Given) 5

8. (a) What is time series? Explain various components of time series. 6

(b) Calculate Fisherâ€™s price index number from the data given below: 4

 CommodityÂ Price per unit (Rs. ) Quantities (Quintal) 2015 2020 2015 2020 A B C D E 6 2 4 10 8 10 2 6 12 1 50 100 60 30 40 56 120 60 24 36

9. (a) What is estimator? Write the characteristics of a good estimator. 2+4=6

(b) Explain null hypothesis and alternative hypothesis. 4

10. (a) Write the definitions of arithmetic mean, median and mode. Mention one use of each of these three measures.Â  6

(b) Given below the mean, median and standard deviation of two distributions. Determine which distribution is more skewed. 4

1. Mean = 22

Median = 24

Standard deviation = 10

1. Mean = 22

Median = 25

Standard deviation = 12

11. (a) What is cost of living index number? Discuss the importance of cost of living index number. 5

(b) A can hit a target thrice in 5 shots, B twice in 5 shots and C thrice in 4 shots. They fire a volley. What is the probability that A and B can hit the target and C cannot hit? 5

OPTION â€“ B

Paper: COM-HG-3026

Full Marks: 80

Time: Three hours

The figures in the margin indicate full marks for the questions.Â

Answer Questions Nos. 1, 2, 3 and any four from the rest.

1. Answer the following as directed: 1×10=10

1. What is network?

2. What is event?

3. What is PERT?

4. What is CPM?

5. The word inventory means _______.Â

6. Write one benefit of controlling inventory.Â

7. Write one limitation of EOQ.Â

8. The set of feasible solutions to an LPP is a _______ set.Â

10. What is ABC analysis?

2. Answer the following in short: 2×5=10

1. What is the difference between ABC analysis and VED analysis?

2. What is graphical method?

3. Define EOQ in inventory control.Â

4. When do we replace an item?

5. What is shortage cost?

3. Answer any four questions: 5×4=20

1. Write the concept of linear programming.Â

2. Solve graphically the linear programming problem (LPP):Â

1. Explain the different types of replacement models.Â

2. Discuss various costs involved in inventory models.Â

3. Group the items given below into an ABC classification:Â

 Item No. 3 4 2 1 7 8 6 5 9 10 Annual Usage: (in 000 Rs.) 75 37 14 36 32 8 16 11 95 4

4. Answer any four questions: 10×4=40

1. XYZ leather company manufactures two types of soccer balls A and B. Each type of ball requires work by both types of employees â€“ semi-skilled and skilled. The semi-skilled employees employ machines in the manufacture of balls while the skilled employees hand-sew the balls. The available time (per week) for each type of employee and the time requirement for each type of balls is given below:Â

 Type of employeeÂ Manufacturing time requirement (in hours) Time availableÂ  (hr/week) Balls A Ball B Semi-skilledÂ  SkilledÂ 3 5 4 7 100 175

The cost of an hour of semi-skilled labour is Rs. 10 and that of an hour of skilled labour is Rs. 16. To meet weekly demand requirements at least 25 balls of type A and at least 20 balls of type B must be manufactured. Formulate this problem as an LPP model to minimise the cost of production.Â

1. Solve by simplex method:Â

1. (1) Construct a network diagram and find the EST and LST for the following data:Â

 JobÂ DescriptionÂ Successor ActivityÂ Time in minutesÂ S A B C D F F Start Proceeding letterÂ  Dictating letterÂ  Order executionÂ  SupervisionÂ  DispatchingÂ  FinishÂ A B D E E F None 0 4 3 7 6 2 0

(2) Write the benefits of replacement problem.Â

1. Explain briefly the replacement of items whose maintenance cost increases with time and the value of money also changes with time.Â

2. Write short notes on:Â

1. Nature and characteristic of O.R.Â

2. The carrying cost or storage cost.Â

1. What are the costs associated with inventory? Distinguish between deterministic and stochastic model in inventory theorem. 4+6=10

2. Write an explanatory note on evolution of operation research.Â

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