## mba-1-sem-mathematics-and-statistics-for-managers-march-2013

mba-1-sem-mathematics-and-statistics-for-managers-march-2013

March 2013

I Semester

(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.

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.

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 :

 Acts Events A B C D S1 50 20 -10 -20 S2 120 50 200 300 S3 200 240 400 350

Tine probabilities of the events are 0.2, 0.5 and 0.3 respectively.