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## Ms-8 Dec 2007

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MS-8   Dec, 2007

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. Distinguish between decision making under certainty and decision making under uncertainty. Mention certain methods for solving decision problems under uncertainty. Discuss how these methods can be applied to solve decision problems.

2. Use Cramer's rule for a 3 x 3 system of linear equations to solve the following system :

2x - y + 3z = -3

-x-y+3z= -6

x-2y-z= -2

3. From the data given below, compute the quartile deviation.

 Monthly wages   (Rs.) No. of workers Below 850 12 850-900 16 900-950 39 950-1000 56 1000-1050 62 1050-1100 75 1100-1150 30 1150 and   above 10

4. the members of a consulting firm rent cars from three rental agencies : 60% from agency l, 30% from agency 2 and 10% from agency 3. if   9% of the cars from agency 1 need a tune-up , 20%. of the cars from agency 2 need a tune-up and 6% of the cars from agency 3 need a tune-up, what is the probability that a rental car delivered to the firm will need a tune-up ?

5. To see whether silicon chip sales are independent of where the US economy is in the business cycle, data have been calculated on the weekly sales of a firm and on whether the US economy was rising to a cycle peak, at a cycle peak, falling to a cycle peak or at a cycle trough. The results are

 High Medium Low Total Economy at peak 20 7 3 30 Economy at   trough 30 40 30 100 Economy rising 20 8 2 30 Economy falling 30 5 5 40 Total 100 60 40 200

6. Write short notes on any three of the following :

(a) Concept of Maxima and Minima

(b) Types of classification of data

(c) Pascal Distribution

(d) Multi-stage sampling & Multi-phase sampling

(e) Box-Jenkins Models for Time Series

7. In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the Delhi half-marathon and found that 13% of them got sick in the two-week period after the marathon. In a second sample of 400 runners who did not participate in the marathon, only 3% were sick in the same two-week period. What would be the null hypothesis ? Find a 9o% confidence interval for the percentage of Delhi half-marathon runners who got sick in the two-weeks after the race.

8. A study by a roadways company on the effect of bus-ticket prices on the number of passengers produced the following results :

 Ticket price   Rs Passengers per   100 km 25 800 30 780 35 780 40 660 45 640 50 600 55 620 60 620

Develop the estimating equation that best describes the data. Predict the number of passengers per 100 miles if the ticket were Rs.10.