Master of Business Administration (MBA) Examination
(Mathematics and Statistics for Managers)
Time 3 Hours) (Max. Marks 80
Note : Attempt any five questions with a minimum of two questions from each section. All questions carry equal marks.
(Section I: Business Mathematics)
1. (a) In an industry comprising 100 firms, the number of firms committing drop-error, go-error, no error and both the errors are in the ratio 9:8:6:3. Find the number of firms committing: (i) drop-error only (ii) both the errors.
(b) If the Cost function and Revenue function of the firm that produces and sells x units of its brand are given by :
C(x) = 5.x + 350 and RCt) = 50x - x2 respectively.
Find : (i) The break even point,
(ii) The qxiantum of production that fetches profit.
2. (a) If
(b) Find the value of
3. (a) Evaluate :
(b) Discuss the continuity of function f(x) = at x = -2.
4. (a) Solve by the Cramer's rule :
x – y – z = 1 = y – z - x = z – x - y.
(b) Find the extreme values of the function :
y = x3 - 6x2 + 9x - 8.
(Section II : Business Statistics)
5. (a) Write a note on application of Statistics in Business and Management.
(b) Define the following event with example :
(i) Mutually exclusive events
(ii) Exhaustive events
(iii) Independent event
(iv) Dependent event.
6. (a) Is there any fallacy in the statement ? The mean of a binomial distribution is 20 and its standard deviation is 7.
(b) What Is Poisson distribution ? Give examples where it can be applied.
7. (a) The coefficient of Rank Correlation of marks obtained by 10 students in English and Mathematics was found to be 0.5. It was later discovered that the difference in ranks in two subjects obtained by one of the students was wrongly taken as 3 instead of 7. Find the correct coefficient of rank correlation.
(b) A student obtained the two regression equations as 2X-5Y-7-0 and 3X+2Y-8=0: Do you agree with him?
8. (a) Find out the seasonal fluctuations by the method of Moving Averages from the following data :
Year Summer Monsoon Autumn Winter
1976 30 81 62 119
1977 33 104 86 171
1978 42 153 99 221
(b) Calculate the expected opportunity loss from the following pay off table and hence decide which act is to be selected :
Tine probabilities of the events are 0.2, 0.5 and 0.3 respectively.