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. Gradable Assignment 2 QUANTITATIVE METHODS FOR MANAGEMENT   ASSIGNMENT 2 ( You can use any statistical software like Excel, Minitab, SAS, SPSS, Matlab….) 1.      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.                                   2.      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   WINDOWS LAPTOPS   Low Medium Medium Low 4 17 17 5 Medium 8 23 22 27 High medium High 10 17 19 11 High High 16 20 14 20 LAPTOPS 3.      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)