Subject Code: 3519906
GUJARAT TECHNOLOGICAL UNIVERSITY
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MBA (PART TIME) SEMESTER 01 - EXAMINATION - SUMMER-2018Subject Name: Business Statistics
Time: 10:30 AM To 01:30 PM Date:04/05/2018
Total Marks: 70
Instructions:
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- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
Q.1 Explain in short 14
- Define Kurtosis.
- State addition & multiplication rule of probability for two events A & B.
- What is Standard Normal Distribution?
- What is discrete and continuous variable?
- What is auto-correlation?
- What are the components of a time series?
- What is Hurwicz Criteria in decision making?
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Q.2 (a) Enlist different types of charts and graphs to display 07
- Qualitative data
- Quantitative data
(b) Calculate Karl Pearson’s coefficient of skewness from the data given below: 07
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| Hourly Wages (Rs.) | No. of Worker | Hourly Wages (Rs.) | No. of Worker |
|---|---|---|---|
| 40-50 | 5 | 90-100 | 30 |
| 50-60 | 6 | 100-110 | 36 |
| 60-70 | 8 | 110-120 | 50 |
| 70-80 | 10 | 120-130 | 60 |
| 80-90 | 25 | 130-140 | 70 |
OR
(b) Find the mean, Median and Mode of the following data 07
| Class | Frequency |
|---|---|
| 300-325 | 5 |
| 325-350 | 17 |
| 350-375 | 80 |
| 375-400 | 227 |
| 400-425 | 326 |
| 425-450 | 248 |
| 450-475 | 88 |
| 475-500 | 9 |
Q.3 A decision maker has a business problem involving four alternatives and four states of nature. The following table shows the profit payoff.
| Alternatives | States of nature | |||
|---|---|---|---|---|
| S1 | S2 | S3 | S4 | |
| A1 | 16 | 10 | 12 | 7 |
| A2 | 13 | 12 | 9 | 9 |
| A3 | 11 | 14 | 15 | 14 |
Assuming that he does not have any knowledge of the probabilities of occurrence of the states of nature, find the decisions to be recommended under each of the following criteria
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- Maximin
- Maximax
- Minimax Regret
Q.4 (a) The probability of a bomb hitting a target is 0.2. Two bombs are enough to destroy a bridge. If six bombs are aimed at the bridge, find the probability that the bridge is destroyed. 07
OR
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(b) A maker of soft drinks is considering the introduction of new brand. He expects to sell 50,000 to 1,00,000 bottles of the new soft drink in a given period according to the following probability distribution. 07
| No. of bottles sold (in '000s) | 50 | 60 | 70 | 80 | 90 | 100 |
|---|---|---|---|---|---|---|
| Probability | 0.13 | 0.20 | 0.35 | 0.22 | 0.08 | 0.02 |
If the product is launched he will have to incur a fixed cost of Rs. 48,000. However each bottle sold would give him a profit of Rs. 1.25. Should he introduce the brand?
Q.4 (a) A manufacturer, who produces medicine bottles, finds that 0.1% of the bottles are defectives. Bottles are packed in boxes containing 500 bottles. A drug manufacturer buys 100 boxes from the producers of bottles. Using Poisson distribution, find how many boxes will contain 07
- No defectives.
- At least 2 defectives.
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(b) Explain different types of correlations with the help of scatter diagrams. 07
OR
(b) From the following data calculate price index numbers for 2010 with 2000 as base year by 1) Paasche’s Method and 2) Marshall-Edgeworth method. 07
| Commodities | 2000 | 2010 | ||
|---|---|---|---|---|
| Price | Quantity | Price | Quantity | |
| 20 | 8 | 40 | 6 | |
| 50 | 10 | 60 | 5 | |
| 40 | 15 | 50 | 15 | |
| 20 | 20 | 20 | 25 | |
OR
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Explain the assumptions of simple linear regression model 07
Q.5 Fit a straight line trend by the method of least squares to the following data: 07
| Year | y |
|---|---|
| 1990 | 242 |
| 1991 | 250 |
| 1992 | 252 |
| 1993 | 249 |
| 1994 | 253 |
| 1995 | 255 |
| 1996 | 251 |
| 1997 | 257 |
| 1998 | 260 |
| 1999 | 265 |
| 2000 | 262 |
Q.5 A departmental store gives in-service training to its salesmen which is followed by a test. It is considering whether it should terminate the services of any salesman who does not do well in the test.
The following data shows the test scores and sales made by nine salesmen during a certain period:
| Test Scores | 14 | 19 | 24 | 21 | 26 | 22 | 15 | 20 | 19 |
|---|---|---|---|---|---|---|---|---|---|
| Sales ('000 Rs.) | 31 | 36 | 48 | 37 | 50 | 45 | 33 | 41 | 39 |
- Calculate the coefficient of correlation between the test scores and the sales. 7
- Estimate the most probable sales volume of a salesman making a score of 28. 7
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OR
- If the firm wants a minimum sales volume of Rs. 30,000, what is the minimum test score that will ensure continuation of service? 7
- Estimate what will be the score if a salesman has achieved a sales of Rs. 55,000. 7
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