Mathematics And Statistics For Managers

1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

End Semester Examinations – OCTOBER 2014

M.I.B. – i semester

MATHEMATICS AND STATISTICS FOR MANAGERS

 

Duration: 3 Hours                                                                                           Max. Marks: 100

Section – A

1. Answer any SEVEN questions. Each carries 5 marks.                                       (7 x 5 = 35)
2. Motors has a weekly profit in Rupees of P(x) = -0.005x³ -0.3x² +900x – 1500 and currently 40 cars are sold per week. What is the profit be if they sell 40  cars? What is the marginal  profit if 40 cars are sold?
3. Mention the steps to calculate multiple regression or multiple correlation by using Excel.
4. Calculate median and mode :

X	1	2	3	4	5	6
f	10	12	16	15	2	1

 

4. Find mode and standard deviation of the following: 4, 9,4,3,10,3, 6,9,4,4
5. The regression coefficients are: bxy = – 0.8 and byx = – 0.7. Calculate the following: a) Correlation Coefficient b) Variation due to other reasons(residuals)(Coefficient of non-determination).
6. The number of accidents in a year attributed to taxi-drivers in a city follows Poisson distribution with mean 3. Out of 1,000 taxi drivers, find the number of drivers with no accident in a year.

 

7. In drawing 1 card from a deck of 52 cards, find the probability that a single draw will be either a face card or a spade card.

 

8. The revival of the M’s Indian economy depends on increase in the world crude oil production and the fall of South East Asian economy excluding India. The probability of increase in oil production is 0.6 and the probability of the fall of the South East Asian Economy excluding India is 0.3. What is the probability of the revival of  M’s Indian  economy?

 

9. Give reasons for the statements given below:
10. Standard deviation can not be negative.
11. If bxy and byx are negative correlation co-efficient is

 

10. A fort had provisions for 300 men for 90 days. After 20 days, 50 more men came to the fort. How long will the remaining food last at the same rate?

 

Section – B

1. II) Answer any three Each carries 15 marks.                         (3 x 15 = 45)

11(a) The electronic fly over is currently charging Rs.30 one way per day. The average number of cars travelling per day is 20,000. The contractor concludes that by increasing toll from Rs.30 to Rs.35 the reduction in number of cars is 800. What toll has to be charged to maximize the revenue?

(b) An apartment complex has 250 apartments to rent. If they rent x apartments then their monthly profit, in dollars, is given by, P(x) = – 8x² + 3,200x – 80,000. How many apartments should they rent in order to maximize their profit?

12. Calculate correlation coefficient between two markets’ share prices prevailing over 7 days from the following data:

Days           :  1    2      3     4     5     6      7

Market A   : 20   22   22   24   26   26    25

Market B   : 20   19    20   21   25   24   24

 

13 (a) A man can complete his work in 24 days by working 5 hours a day. How many days will he take to complete the same work; working 8 hours a day?

1. b) Cost of 6 identical articles is Rs.(2x+3) and the cost of 10 similar articles is Rs. (4x-5). Find the value of x.
2. Six men can do a certain piece of work in (5x+6) days and 11 men can do the same work in 3x days. Find the value of x.

14 (a) Vehicles pass through a junction on a busy road at an average rate of 300 per hour.

1. Find the probability that none passes in a given minute.
2. What is the expected number passing in two minutes?

• Find the probability that this expected number actually pass through in a given two-minute period.

1. b) A company makes electric motors. The probability an electric motor is defective is 0.01. What is the probability that a sample of 300 electric motors will contain exactly 5 defective motors?
2. Calculate Fisher’s index and the % of inflation from the following information.

Base Year		Current year
Price	Quantity	Price	Quantity
40 50 35 20	5 8 3 2	45 52 40 18	6 8 4 2

 

Section – C

III) Compulsory question.                                                                                  (1 x 20 = 20)

16. Interpret the results “highlighted in dark letter” obtained from four PG subjects of 28 students’ internal marks of MIB students (Batch: 2014-15) by using statistical package.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.806922108
R Square	0.651123289
Adjusted R Square	0.441797262
Standard Error	1.294066541
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	3	15.62695894	5.208986	3.11057	0.126752393
Residual	5	8.373041063	1.674608
Total	8	24
	Coefficients	Standard Error	t Stat	P-value				Upper 95.0%
Intercept	3.910934467	1.069707213	3.656079	0.014655				6.660704
X Variable 1	-0.09064735	0.053720666	-1.68738	0.152335				0.047446
X Variable 2	-0.00614618	0.008670235	-0.70888	0.510071				0.016141
X Variable 3	0.000449966	0.000240479	1.871127	0.120239				0.001068
RESIDUAL OUTPUT
Observation	Predicted Y	Residuals
1	2.040913567	-0.040913567
2	2.684068942	0.315931058
3	4.613398238	-0.613398238
4	5.008443849	-0.008443849
5	5.966746968	0.033253032
6	6.154403199	0.845596801
7	4.907444762	-1.907444762
8	4.173244289	1.826755711
9	3.451336185	-0.451336185