MBA 1 sem Mathematics and Statistics for Managers Dec 2016
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 a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many do like tennis only and not cricket ? Also find how many people like tennis ?
(b) A garment manufacturer is involved in a fixed cost of Rs. 1.5 lacs and variable cost of Rs. 150 for each shirt. If each shirt can be sold for Rs. 350 then find :
(i) Cost function (ii) Revenue function (iii) Profit function (iv) Break even point.
2. (a) Solve :
(b) Discuss the continuity of given function f at x = 1 and at x = 2 where function f is defined as : •
x+1 when -1<= x <= 1
x when 1<= x <= 2
4-x when 2<= x <=5
3. (a) Given cost function 'C' = 300x -10x2 + (-1/3) x3 where 'x' is output Find for what value of 'x' the Marginal-Cost is minimum.
(b) If Demand function : p = 10 - q - q2 and Supply function : p = q + 2 then calculate consumer-surplus and producer-surplus at equilibrium-price.
. 4. (a) Find the amount of annuity of Rs. 2,000 payable at the end of each 3 months for 6 yrs, if the money is worth 8% per annum, compounded quarterly. Use : [ (1.02)12 = ]
(b) Solve the given equations by Matrix-method [X = A-1B] where X. A and B are matrices. Given :
8x + 4y + 3z = 18
2x + y + z = 5
x + 2y + z = 5.
5. Define Statistics. Explain scope, importance in different Business fields and limitations of Statistics.
6. (a) Customer's account has an average balance of Rs. 480 and standard deviation of Rs, 160. Assuming that account balance is normally distributed, find :
(i) What proportions of account is over Rs. 600 ?
(ii) What proportions of account is between Rs. 400 and Rs. 600?
(iii) What proportions of the accounts, is between Rs. 240 and Rs. 360 ?
(b) Explain with examples and formulas and applications of :
(i) Addition theorem of Probability
(ii) Multiplication theorem of Probability • •
(iii) Conditional Probability
(iv) Baye's theorem.
7. (a) Comment on degree of Correlation between sales and expenses using Karl-Pearson Coefficient of Correlation. Given :
Sales '000 : 50 50 55 60 65 65 65 60 60 60
Expenses '000 : 11 13 14 16 16 15 15 14 13 13
(b) Given : Coefficient of Correlation = 0.9.
Calculate from given data : (i) Two Regtession Equations and Lones (ii) Estimate Sales for Advertising Budget of 20 crore. (iii) For Sales Target of 70 crore's estimate Advertising Budget.
Sales Advertising Expenditure
(Rs. crores) (Rs. crores)
Average 50 10
Standard Deviation 10 2
8 (a) Fit a trend line to the following data by least squares method and calculate trend values for every year :
Year 1985 1987 1989 1991 1993
Production '000 (tons) 18 21 23 27 16
Also estimate the production in the year 1995 and 1997.
(b) If unit of product made is sold. Rs. 5 is gained and if it is un-sold. Rs. 3 is loss incurred. From the given data :
(i) Calculate how many units to be produced to maximise gain? Given : pay-off = [5 x units sold - 3 x units on-sold)
(ii) Calculate EMV (Expected Monetary Values): Given
No. of Units Demanded 0 1 2 3 4. 5 or more
Probability (Distribution Values) 0.2 0.2 0.25 0.30 0.05 0