MODEL QUESTION PAPER
Business Statistics and Analytics (18MBA14)
Part A
Note: Answer any 4 full questions from Q.No. 1 to Q.No. 7
Part Q.No. 8 is compulsory
1 a. Discuss the importance of business analytics? marks)
b. The following distribution gives the pattern of overtime work done by 100 employees of a
company. Find the mean and median? marks)
Overtime 10-15 15-20 20-25 25-30 30-35 35-40
No. of employees 11 20 35 20 8 6
c. The mean of the number of sales of cars over a 3 month period is 87, and the standard
deviation is 5. The mean of the commissions is Rs. 5225 and the standard deviation is Rs.733.
Compare the variations of the two. State the conclusions drawn? (10 marks)
2 a. Give the formulas for Karl Pearson's correlation and Spearman's Rank correlation
(3marks)
b. Explain the difference between PERT and CPM marks)
c. Consider the following data, obtain the two regression equations.
X 6 2 10 4 8
Y 9 11 5 8 7
Also, estimate Y when X is equal to 20. (10 marks)
3 a. What is Binomial distribution and mention its formula? (3marks)
b. The prices of tea company shares in Mumbai and Kolkata for last 10 months are recorded
below. Determine in which market the share price show less variability .
Month Jan Feb March April May June July Aug Sept Oct
Mumbai 105 120 115 118 130 127 109 110 104 112
Kolkata 108 117 120 130 100 125 125 120 110 135
c. The mean and standard deviation of wages of 1000 workers engaged in a factory are
Rs.1200 and 400 respectively. Assuming the distribution to be normal, estimate
Percentage of workers getting wages above Rs.1600.
Number of workers getting wages between RS.600 and Rs.900.
The area under normal curve for different Z are given below
Z 0.5 0.75 1 1.5
Area 0.1915 0.2734 0.3413 0.4332
4 a. Define time series analysis Mention the methods used for the study and measurement of
trend in a time series? (3marks)
b. From the following series of annual data, find the trend line by the method of semiaverages.
Also estimate the value for 1999
Year 1990 1991 1992 1993 1994 1995 1996 1997 1998
Actual Value 170 231 261 267 278 302 299 298 340
c. The sales of a company in million of rupees for the year 1994 2001 are given below
Year 1994 1995 1996 1997 1998 1999 2000 2001
Sales 550 560 555 585 540 525 545 585
Find the linear trend equation?
Estimate the sales for the year 1993?
(iii)Find the slope of the straight line trend?
(iv)Do the figures show a rising trend or a falling trend?
5 a. Illustrate merge and burst events in network analysis
b. Use graphical method, find the maximum value of, Z=5X1 +7X2
subject to the constraints
X1+X2 4
3X1+8X2 24
10X1+7X2 35
X1,X2 0 7marks)
c.
6 a. What do you mean by correlation? Mention any four uses of it? Marks)
b.
C.
In a factory turning out fan blades there is a small change of 0.002 for any blade to be defective.
The blades are supplied in packets of 10. Use Poisson distribution to calculate the approx number
of packets containing no defective, one defective and two defective blades respectively in a
consignment of 10,000 packets. (10 Marks)
7. a. What is Poisson's distribution? Write a formula for probability function of Poisson's
distributions. Marks)
b. A manufacturer employs three inputs: man hours, machine hours and cloth material to
manufacture two types of dresses. Type A dress fetches him a profit of Rs. 160 per piece, while
type that of Rs. 180 per piece. The manufacturer has enough man hours to manufacture 50
pieces of type A or 20 pieces of type B dresses per day while the machine hours ha possesses
suffice only for 36 pieces of type A or for 24 pieces for type B dresses. Cloth material available
per day is limited but sufficient enough for 30 pieces of either type of dress. Formulate the linear
programming problem. Marks)
c.
8. Case Study Compulsory
a. The daily wages of 1000 workmen are normally distributed around a mean of Rs. 70 and with
a standard deviation of Rs.5. Estimate the number of workers whose daily wages will be
between Rs.70 and 72; ii) between Rs.69 and 72; iii) more than Rs.75; iv) less than Rs.63.
(10 Marks)
b.