Quantitative Methods for Management
1. At one of the Management Institutes, a sample of 55 second Year MBA students was selected, and information gathered relating to their age, background of graduation, work experience prior to joining MBA, CGPA score at the end of First Year, and area of specialization. The collected data is given below:
|
No.
|
CGPA
|
Background
|
Specialisation
|
Work Experience
|
Age (in years)
|
|
1
|
3.24
|
Commerce
|
Finance
|
12
|
23
|
|
2
|
3.14
|
Commerce
|
Finance
|
1
|
21
|
|
3
|
3.72
|
Commerce
|
Finance
|
2
|
23
|
|
4
|
3.06
|
Commerce
|
Finance
|
4
|
21
|
|
5
|
3.14
|
Commerce
|
Finance
|
27
|
22
|
|
6
|
3.14
|
Commerce
|
Finance
|
22
|
23
|
|
7
|
3.06
|
Commerce
|
Finance
|
0
|
22
|
|
8
|
3.17
|
Commerce
|
Finance
|
3
|
21
|
|
9
|
2.97
|
Commerce
|
Finance
|
2
|
22
|
|
10
|
3.14
|
Commerce
|
Finance
|
4
|
23
|
|
11
|
3.69
|
Commerce
|
Finance
|
12
|
24
|
|
12
|
2.85
|
Commerce
|
Finance
|
38
|
25
|
|
13
|
2.92
|
Commerce
|
Marketing
|
24
|
23
|
|
14
|
2.79
|
Commerce
|
Marketing
|
33
|
25
|
|
15
|
3.22
|
Commerce
|
Marketing
|
9
|
22
|
|
16
|
2.87
|
Commerce
|
Marketing
|
5
|
22
|
|
17
|
3.14
|
Commerce
|
Marketing
|
10
|
22
|
|
18
|
3.17
|
Commerce
|
Marketing
|
14
|
23
|
|
19
|
3.22
|
Economics
|
Finance
|
18
|
26
|
|
20
|
2.58
|
Economics
|
Finance
|
2
|
25
|
|
21
|
3.36
|
Economics
|
Finance
|
12
|
22
|
|
22
|
3.17
|
Economics
|
Marketing
|
13
|
21
|
|
23
|
2.59
|
Economics
|
Marketing
|
11
|
24
|
|
24
|
2.97
|
Engineer
|
Human Resources
|
104
|
31
|
|
25
|
2.92
|
Engineer
|
Marketing
|
5
|
23
|
|
26
|
3.03
|
Engineer
|
Marketing
|
10
|
23
|
|
27
|
2.79
|
Engineer
|
Marketing
|
22
|
25
|
|
28
|
2.77
|
Engineer
|
Marketing
|
3
|
23
|
|
29
|
2.97
|
Engineer
|
Marketing
|
21
|
25
|
|
30
|
3.11
|
Engineer
|
Marketing
|
32
|
27
|
|
31
|
3.33
|
Engineer
|
Marketing
|
14
|
24
|
|
32
|
2.65
|
Engineer
|
Marketing
|
7
|
23
|
|
33
|
3.14
|
Engineer
|
Marketing
|
2
|
24
|
|
34
|
2.97
|
Engineer
|
Marketing
|
6
|
23
|
|
35
|
3.39
|
Engineer
|
Marketing
|
24
|
24
|
|
36
|
3.08
|
Engineer
|
Marketing
|
3
|
23
|
|
37
|
3.3
|
Engineer
|
Marketing
|
33
|
27
|
|
38
|
2.94
|
Engineer
|
Marketing
|
9
|
24
|
|
39
|
3.25
|
Engineer
|
Marketing
|
2
|
23
|
|
40
|
3.14
|
Engineer
|
Systems
|
3
|
23
|
|
41
|
3.36
|
Engineer
|
System
|
22
|
26
|
|
42
|
2.95
|
Information
|
Finance
|
20
|
24
|
|
43
|
2.98
|
Technology
|
Finance
|
5
|
23
|
|
44
|
2.82
|
Information
|
Marketing
|
13
|
24
|
|
45
|
2.98
|
Information
|
Marketing
|
35
|
26
|
|
46
|
3.33
|
Information
|
Marketing
|
2
|
24
|
|
47
|
2.96
|
Information
|
Marketing
|
45
|
27
|
|
48
|
3.67
|
Information
|
System
|
23
|
25
|
|
49
|
3.22
|
Science
|
Finance
|
18
|
25
|
|
50
|
3.14
|
Science
|
Finance
|
8
|
22
|
|
51
|
3.17
|
Science
|
Finance
|
42
|
26
|
|
52
|
3.25
|
Science
|
Resources
|
0
|
21
|
|
53
|
3. 10
|
Science
|
Marketing
|
2
|
22
|
|
54
|
2.85
|
Science
|
Marketing
|
35
|
24
|
|
55
|
3.25
|
Science
|
Marketing
|
2
|
22
|
a. Present the above data with the help of tables, charts and graphs.
b. Calculate the measures of location and dispersion of CGPA, age and work experience for all backgrounds and specializations. Combine these measures, wherever possible, for all the backgrounds and specializations separately. Discuss the findings.
c. Study and comment on correlations between CGPA and age for students of all backgrounds viz. commerce, science etc.,
d. Summarize your findings and present a managerial report.
( You can use any statistical software like Excel, Minitab, SAS, SPSS, Matlab....)
2. The annual number of industrial accidents occurring in a particular manufacturing plant is known to follow a Poisson distribution with mean 12.
a. What is the probability of observing exactly 12 accidents during the coming year?
b. What is the probability of observing no more than 12 accidents during the coming year?
c. What is the probability of observing at least 15 accidents during the coming year?
d. What is the probability of observing between 10 and 15 accidents ( inclusive) during the coming year?
e. Find the smallest integer "k" such that we can be at least 99% sure that the annual number of accidents occurring will be less than k.
3. Big Office, a chain of large office supply stores, sells a variety of windows and Mac laptops. Company executives what to know whether the demands for these two types of computers are related in any way. They might act as complementary products, where high demand for Windows laptops accompanies high demand for Mac laptops (computers in general are hot), they might act as substitute products (demand for one takes away demand for the other), or their demands might be unrelated. Because of limitations in its information system, Big Office does not have the exact demands for these products. However, it does have daily information on categories of demand, listed in aggregate (that is, over all stores). Each day's demand for each type of computer is categorized as Low, Medium Low, Medium High or High. From the following data, test whether demands for Windows laptops is independent of demand for Mac laptops. (Hint: use Chi square ). Test at 5% level of significance
4. Suppose the annual returns on XYZ stock follows a normal distribution with mean 12% and standard deviation 30%.
a. What is the probability that XYZ's value will decrease during a year?
b. What is the probability that the return on XYZ during a year will be at least 20%?
c. What is the probability that the return on XYZ during a year will be between -6% and 9%?
d. There is a 5% chance that the return on XYZ during a year will be greater than what value?
e. There is a 1% chance that the return on XYZ during a year will be less than what value?
f. There is a 95% chance that the return on XYZ during a year will be between which two values (equidistant from the mean)