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### QUANTITATIVE TECHNIQUES FOR MANAGERIAL DECISIONS

ASSIGNMENT – I
1. (a) What are the requisites of a good classification?
(b) State and prove additive law of probability.
(c) Explain sampling distribution and standard error.
(d) Explain cyclical variation.
(e) Define :
(i) One tail test
(ii) Two tail test
(iii) Critical region.
(f) Explain secondary data.
2. Explain Mean, Median and Mode.
3. (a) State and prove Baye's theorem.
(b) A bag contains 8 white and 6 red balls. Find the probability of drawing two balls of the same colour.
4. Discuss the formulation and testing the validity of hypothesis.
ASSIGNMENT - II
5. (a) Find the inverse of the matrix
ú ú ú
û
ù
ê ê ê
ë
é
=
1 3 4
1 4 3
1 3 3
A
(2DEMB 5)
(b) Show that the matrix A satisfies the equation A2 - 4A + I =0 .
6. A sample analysis of examination results of 200 MBA's was made. It was found that 46 students had
failed, 68 secured a third division, 62 secured a second division and the rest were placed in first division.
Are these figures commensurate with the general examination result which is in the ratio of 4 : 3 : 2 : 1 for
various categories respectively?
7. The following table gives the marks detained in English and Mathematics by 8 students .
Marks in English : 44 42 40 52 39 32 24 46
Marks in Maths : 24 25 28 29 32 35 36 41
(a) Compute the coefficient of correlation for the above data.
(b) Find the equations of regression lines.
8. (a) An insurance salesman sells policies to 5 men all of identical age and good health. According to the
actuarial tables the probability that a man of this particular age will be alive 30 years hence is 3
2 .
Find the probability that 30 years hence
(i) At least 1 man will be alive
(ii) At least 3 men will be alive.
(b) A market research organisation wants to determine on the basis of the following information,
whether there is a relationship between the size of a tooth paste which a shopper buys and the
number of persons in the shopper's House Hold (SH)
No. of person in S.H 1-2 3-4 5-6 7 or more
Size of tube giant : 23 116 78 43
Large : 54 25 16 11
Small : 31 68 36 8
Is there a relationship at 1% level of significance?