MS8 june, 2007
MS8 : 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
xy+3z= 6
x2yz= 2
3. From the data given below, compute the quartile deviation
Monthly wages (Rs) 
No. of workers 
Below 850 
12 
850900 
16 
900950 
39 
9501000 
56 
10001050 
62 
10501100 
75 
11001150 
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 tuneup 20%. of the cars from agency 2 need a tuneup and 6% of the cars from agency 3 need a tuneup, what is the probability that a rental car delivered to the firm will need a tuneup ?
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 

100 
60 
40 
200 
State the null hypothesis. At 0.10 significance level, what is your conclusion ?
(Given the tabulated value of test statistic is 10.645)
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) Multistage sampling & Multiphase sampling
(e) BoxJenkins 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 halfmarathon and found that 13% of them got sick in the twoweek 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 twoweek period. What would be the null hypothesis ? Find
a 9o% confidence interval for the percentage of Delhi halfmarathon runners who got sick in the twoweeks after the race.
8. A study by a roadways company on the effect of busticket 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.