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Ms-8 Question bank

Ms-8 Question bank (10)

Ms-8 Question bank

Saturday, 10 November 2012 16:21

Ms-8 june 2010

Written by

MS-8   june, 2010

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. A car is purchased for Rs. 300,000. If the depreciation for the first three years is at 10% per annum and for the next two years is at 20% per annum, then calculate the

depreciated value of the car at the end of five years.

2. Units A, B, C of a factory manufacture 25%, 35%, 40% respectively of the total cars.

Out of their output, 5%, 4%, 2% defective cars came from the units A, B, C respectively.

Using Baye's Theorem or otherwise, find the probability that a randomly selected car

found defective has come from the unit A.

3.Explain the term Random variable associated with an Experiment. Thereafter distinguish between discrete and continuous probability distributions also mentioning two discrete and two continuous distributions.

4. Compute the Quartile Q3, Decile D5, Percentile P50 and interpret these values in lines 1— 3 for the grouped data showing profits of 100 companies in a year in the table given below :

Profit in lakh Rupees

Number of Companies +

20-30

20

30-40

10

40-50

15

50-60

15

60-70

40

5. The breaking strength X of cables in a factory has a normal distribution with a mean of p.=1800 lbs and a standard deviation of v = 100 lbs. It is claimed that the breaking

strength X can be increased by the introduction of a new technique in the manufacturing

process. Should we accept the claim on the basis of a sample of 50 cables manufactured

under the new technique; at a significance level of a = .05 given that the mean breaking

strength for the sample is mean = 1850 with the standard deviation remaining the same.

(For convenience, we are giving the result P (Z <=1.645) = .95 where Z has the standard

normal distribution N (0,1)).

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

a) Primary and secondary data

b) Arithmetic Mean and Median of data

c) Sample space associated with an experiment

d) Linear function

(e) Sampling with and without replacement explaining them, mentioning their scope, drawing graphs and giving examples wherever possible.

7. Using the method of least squares, find the regression equation of y on x for the data   given in the Table below :

x

1

2

3

4

5

y

5

7

9

10

11

And from the regression equation obtained, find the value of y corresponding to x = 2.5.

8. Solve the system of non-homogeneous linear equations :

x1 +x2 +2 x3= 2

3x1 — x2+ x3 = 6

-x1+ 3 x2 +4x3=4

by any one method out of cramar's rule, Inverse Matrix method, Gauss-Jordan method.

Saturday, 10 November 2012 16:18

Ms-8 june 2011

Written by

MS-8   june, 2011

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

  1. You are given the frequency distribution of 292       workers of a factory according to their average weekly income. Calculate quartile deviation and its coefficient from the following data :

 

Weekly Income

(Rs.)

No. of workers

Below 1350

8

1350-1370

16

1370-1390

39

1390-1410

58

1410-1430

60

1430-1450

40

1450-1470

22

1470-1490

15

1490-1510

15

1510-1530

9

1530 and above

10

2. The Herr- McFee Company, which produces nuclear fuel rods, must X-ray and inspect each rod before shipping. Karen Wood, an inspector, has noted that for every, 1,000 fuel rods she inspects, 10 have interior flaws, 8 have casing flaws, and 5 have both flaws. In her quarterly report, Karen must include the probability of flaws in fuel rods. What is the probability ?

3. The manager of a small postal substation is trying to quantify the variation in the weekly demand for mailing tubes. She has decided to assume that this demand is normally distributed. She knows that on average 100 tubes are purchased weekly and that 90 percent of the time, weekly demand is below 115. What is the standard deviation of this distribution ?

4. The mean length of life of a certain cutting tool is 41.5 hours with a standard deviation of 2.5 hours. What is the probability that a simple random sample of size 50 drawn from this population will have a mean between 40.5 hours and 42 hours ?

5. Before an increase in excise duty on tea, 400 people out of a sample of 500 people were found to be tea drinkers. After an increase in duty, 400 people were tea drinkers in a sample of 600 people. State, whether there is a significant decrease in the consumption of tea. You may use a 5% level of significance.

6. Write short notes on any three of the following

(a) Central Limit Theorem

(b) Stratified Sampling

(c) Less than type Ogive

(d) Level of significance

(e) Coefficient of variation

7. Below are given the figures of production (in m. tonnes) of a sugar factory :

Year

2002

2003

2004

2005

2006

2007

2008

Production

(in m. tonnes)

80

90

92

83

94

99

92

 

Estimate a linear trend equation and use it to forecast the production for 2009

 

8. The demand equation faced by DuMont Electronics for its personal computers is given by

P= 10,000 — 4Q, where P= price per unit and

Q= quantity demanded.

(a) Write the marginal revenue equation.

(b) At what price and quantity will marginal revenue be zero ?

(c) At what price and quantity will total revenue be maximized ?

(d) Find the price elasticity of demand at P = 6,000.

Saturday, 10 November 2012 16:16

Ms-8 Dec 2007

Written by

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.

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