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Quantitative Techniques in Management (VVN)

1 . What do you understand by a Linear Programming Problem? What are its limitations? Discuss briefly the applications of linear programming in any functional area of management.

2 . Solve the following transportation problem for optimal solution.

W1 W2 W3 W4 W5 quantity

P1 20 28 32 55 70 50

P2 48 36 40 44 25 100

P3 35 35 22 45 48 150

Demand 100 70 50 40 40

3 . What is the Hungarain mathod for the assingnment problem ?

4 . What do you mean by correlation? Explain various type of correlation with the help of examples .

5 . What is the probability of getting a sum ‘FOUR’ when two dice are thrown .

6 . Discuss various components of time series with the help of examples.

7 . For the given of a random variable x and associated probabilities ( given in rows 1 and 2 of the following table ) work out the variance and standard deviation

X 2 3 4 5 6 7 8 9 10 Total

P(x) .05 .10 .30 .20 .05 .10 .05 .10 .05 1.00

8 . Boys of a certain age are known to have a mean weight of μ = 45 Kilograms. A complaint is made that the boys living in a municipal children’s home are underfed. As one bit of evidence, n = 50 boys (of the same age) are weighed and found to have a mean weight of x¯¯ = 41.5 Kilograms. It is known that the population standard deviation σ is 5.6 Kilograms (the unrealistic part of this example!). Based on the available data, what should be concluded concerning the complaint?

Case Detail :

The length of life of an instrument produced by a machine has a normal ditribution with a mean of 14 months and standard deviation of 2.5 months. Find the probability that an instrument produced by this machine will last

1. between 10 and 14 months.

2. less than 10 months.

3. more than 10 months

1. Scatter diagram is also called _________________

Correlation graph

Dot Chart

Zero correlation

None of these

2. Correlation can be ____________________________________________

Positive only

Positive or negative

Negative only

None of these

3. In correlation analysis, P.E. = ________________. x 0.6745

Standard Error

Probable Error

Correlation analysis

None of these

4. Regression lines are also called ________________________.

Correlation graph

Scatter diagram

Estimating lines

None of these

5. The arithmetic mean of bxy and byx is ____________________________.

Equal to 1

Equal to 2

Greater than r

Less than r

6. ____________________________. refers to the chance of happening or not happening of an event.

Regression

Probability

Correlation

None of these

7. An event whose occurrence is impossible, is called ______________________

Sure event

Impossible event

Uncertain event

None of these

8. If two events, A and B are not mutually exclusive, the P(AUB) = __________________

P(A) + P(B)

P(A) + P(B) – P(A and B)

P(A) + P(B) + P(A and B)

None of these

9. The definition of priori probability was originally given by ____________________________

De-Moivre

Laplace

Pierre de Fermat

James bernoulli

10. Three dies are thrown, probability of getting a sum of 3 is ____________________.

3/216

(2/3)

(3/36)

1/216

11. Binomial distribution is a ________________________________ probability distribution

Discrete

Continuous

Continuous distribution

None of these

12. When probability is revised on the basis of all the available information, it is called ____________.

Priori probability

Continuous

Posterior probability

None of these

13. The height of persons in a country is a ________________________. random variable.

Discrete

Continuous

Discrete as well as continuous

None of these

14. For a binomial distribution with probability p of a success and of q of a failure, the relation between mean and variance is ____________________________.

Mean is greater than variance

Mean is less than variance

Mean is equal than variance

Mean is greater than or equal to variance

15. In a binomial distribution, if n =8 and p = 1/3, then variance = ________________________

(16/9)

(8/3)

48/3

64/3

16. Poisson distribution is the limiting form of ______________________________.

Poisson

Binomial distribution

Normal distribution

None of these

17. Poisson distribution is a ____________________________probability distribution.

Discrete

Continuous

Poisson

None of these

18. In Poisson distribution, the value of ‘e’ = __________________________

282

718

1.718

2.718

19. Mean and variance of Poisson distribution is equal to ______________________________.

nq

e

m

npq

20. __________________________.distribution gives a normal bell shaped curve.

Poison

Binomial

Normal

None of These

21. The height of normal curve is at its maximum at the ______________________.

Mean

Mode

Medain

None of these

22. Normal distribution is ______________________

Continuous

Unimodal

Symmetrical

All of these

23. An approximate relation between MD about mean and SD of a normal distribution is

5MD = 4 SD

3MD = 3 SD

3MD = 2 SD

4MD = 5 SD

24. In a ________________________. distribution, quartiles are equi-distant from median

Poison

Normal

Binomial

None of These

25. A normal distribution requires two parameters, namely the mean and ______________

Standard deviation

mean deviation

Mode

Medain

26. Mean ± 2 S.D. covers ______________.% area of normal curve.

95.45

98.73

68.27

95.54

27. A __________________________ is a function of sample values.

Statistic

Parameter

Population

None of these

28. Test of hypothesis and ________________________ are the two branches of statistical inference

Probability

Statistical analysis

Estimation

None of these

29. Quartile deviation of normal distribution is equal to ____________________

2/3 S.D.

4/5 S.D.

3/4 S.D.

1 S.D.

30. Type I error is denoted by the symbol ________________________________.

Alpha

Beta

Gramma

None of these

31. A sample is treated as large sample when its sample size is ____________________________

More than 30

More than 100

More than 20

More than 50

32. Degrees of freedom for Chi-square in case of contingency table of (4×3) order are __________________.

6

7

8

9

33. By test of significance , we mean ____________________________

A significant procedure in statistics

A method of making a significant statement

A rule of accepting or rejecting hypothesis

A significant estimation problem

34. When sample is small, ________________________ test is applied.

z- test

y- test

i- test

t- test

35. Who developed F-test ?

R.A. Fischer

Karl Pearson

James Bernoulli

Charles Babage

36. Chi-square test was developed by __________________

R.A. Fischer

Karl Pearson

William Gosset

James Bernoulli

37. In a normal curve, the significance level is usually termed as ______________________region

Acceptance region

Critical region

Level of acceptance

None of these

38. Chi-square test was first used by____________________________

R.A. Fischer

Karl Pearson

William Gosset

James Bernoulli

39. If two samples of size 9 and 11 have means 6.8 and 8.8, and variance 36 and 25

respectively, then value of t = ____________________.

0.79

1.79`

2.79

None of these

40. In one way ANOVA, the variances are ______________________

Between samples

Within samples

Both 1&2

Neither 1 nor 2 option

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