Seat No.:
Enrolment No.
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GUJARAT TECHNOLOGICAL UNIVERSITY
MBA - SEMESTER 01- EXAMINATION - SUMMER-2018
Subject Code: 3519207
Subject Name: Business Statistics (BS)
Time: 10:30AM To 1:30 PM
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Date:04/05/2018
Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 Explain following terms 14
- coefficient of variation
- marginal probability
- multicollinearity
- autocorrelation
- family budget and cost of living index
- cyclical variations
- Random experiment
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Q.2 A. Find mean, median and mode for following data 07
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| 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 |
B. Write a note on decision theory 07
OR
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 07 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?
B 1. 1555 2. 15%5 07
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OR
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 |
Q.4 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
B 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 0f 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. 07
| 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 |
Q.5 A Write a detail note on correlation and regression. Discuss difference between simple regression and multiple regression using example. 07
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OR
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, 07
- What percentage will have lifetime of 350 hours or less?
- What percentage will have lifetimes from 220 or 260 hours?
B Fit the trend line and calculate trend for the year 1960. 07
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| X | Y |
|---|---|
| 1950 | 28 |
| 1951 | 35 |
| 1952 | 42 |
| 1953 | 10 |
| 1954 | 22 |
| 1955 | 39 |
| 1956 | 28 |
Consider following observations: 14 123,250,352,143,112,324,256,235,412,156 Prepare five point summary Prepare box and whisker plot
OR
Find mean and standard deviation Find range, P80 and D7.
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