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## Ms-8 Question bank (10)

Ms-8 Question bank

Saturday, 10 November 2012 16:26

### Ms-8 june 2007

MS-8   june, 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 40 100 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) 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.

Saturday, 10 November 2012 16:24

### Ms-8 june 2008

MS-8   june, 2008

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. What factors       in modern society contribute to  the increasing importance of quantitative approach to  management ? List one applicaticn of quantitative techniques in each functional area of  management.

2. The demand for a certain product is represented by the equation p : 20 + 5q

-q2 where q is the number of units demanded and p is the price per unit. Find marginal revenue function. What is the marginal revenue at q = 2 ?

3 From the frequency distribution, find the standard deviation using the formula fcr the grouped data :

 Class Interval frequency 10-20 9 20-30 18 30-40 31 40-50 17 50-60 16 60-70 9 Total 100

4. A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is ruste,C or a bolt ?

5. In a study to test whether there is a difference between the average height of adult females born in two different countries, random samples yielded the following results :

n1= 120 , mean of x1= 62.7 , and s1=2.5

n2= 150 , mean of x2= 61.8 , and s2=2.62

where the measurements significance to test the heights. are in inches. Use 0.05 level of difference between the  average heights

6. Write short notes on any threeof the following :

(a) Step functions

(b) significance of Measures of Dispersion

(c) Criteria of Optimism

(di The F disiribution

e)Auto-regressive (AR) models

7. Given below are figures of production (in thousand kilos) for a sugar factory. Obtain the secular trend by fitting a straight line.

8.Find the area under the standard normal curve, which lies

(a) to the left of z= 0.94

(b) to the right of z= 0.65

 Years 2000 2001 2002 2003 2004 2005 2006 Production 12 10 14 11 13 15 16

(c) to the right of z =1.76

(d) between z =0.34 and z =0.62

Saturday, 10 November 2012 16:22

### Ms-8 june 2009

MS-8   june, 2009

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. An analysis of the hourly wages paid to workers in two firms A and B belonging to the same industry gives the following results :

 Firm A Firm B Number of wage earner 586 648 Average hourly   wage 52.5 47.5 Variance of the distribution of wage 100 121

2. Which firm, A or B pays out the larger amount as hourly wages ? In which firm A or B, is there greater variability in individual wages ? Bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. One ball is d.rawn

at random from one of the bags and is found to be red. Find the probability that it was drawn from bag A.

3.What do you understand by probability sampling ? Describe stratified and cluster sampling designs. Vhat is the difference between a cluster and a strata ?

4. A course in Quantitative Applications is taught to 12 students by conventional classroom procedure. A second group of 10 students was given the same course by programmed materials. The same examination was given to each Soup at the end of the course. The 12 classroom sfudents scored 85 marks on an average with the standard deviation 4, while 10 students using programmed material scored SL marks on an average with a standard deviation of 5. Test whether the two methods of learning are equally effective ? Use 0.10 level of significance.

5.The information given below relates to the advertisement and sales of a company (in lakhs of Rupee) :

 Advertisement Expendifure (X) Sales (Y) Arithmetic Mean 20 100 Standard Deviation 3 12

Correlation coefficient between X & Y = 0.8

(a) Find the two regression equations.

(b) What should be the advertisement expenditure if the company wants to attain sales target of Rs 120 lakhs ?

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

(a) Marginal Revenue

(b) Exponential Smoothing

(c) Less than type Ogive

(d) Probability densify tunction (pdf)

(u) Significance level

7. In a random sample of 500 people of a ctty, it was found that 160 preferred seafood. Find a 95% confidence interval for the actual proportion of people who preferred seafood.

8. Solve the following system of linear equations using matrices :

2x+3y+3z=5

x-2y+z= -4

3x-y-2z= 3

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