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## Quantitative Methods for Management

ASSIGNMENT                                        Answer all the questions                                             Max. Marks: 40

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 are indicated in the file management.xls:

(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.                                                                15 MARKS

1. Olive Construction Company is determining whether it should submit a bit for a new shopping center. In the past, Olive’s main competitor, Base Construction Company, has submitted bids 70% of the time. If Base Construction Company does not bid on a job, the probability that Olive Construction Company will get the job is 0.50. If the Base Construction Company bids on a job, the probability that Olive Construction Company will get the job is 0.25.

(a)  If Olive Construction Company gets the job, what is the probability that Base Construction Company did not bid?

(b)  What is the probability that Olive Construction Company will get the job?                            10 MARKS

1. An investor is concerned with the market return for the coming year, where the market return is defined as the percentage gain (or loss, if negative) over the year. The investor believes there are five possible scenarios for the national economy in the coming year- rapid expansions, moderate expansions, no growth, moderate contractions and serious contraction. Furthermore, she has used all of the information available to her to estimate that the market returns for these scenarios are, respectively 23%, 18%,15%,9% and 3% .Also she has assessed the probabilities of these outcomes are 0.12, 0.40,0.25, 0.15 and 0.08. Use this information to describe the probability distribution of the market return. Calculate, average return, standard deviation and variance of the probability distribution of the market return for the coming year and comment.    5 MARKS

1. An American consumer organization is currently examining the relationship among several variables including gasoline mileage as measured by miles per gallon; the horsepower of the car’s engine and the weight of the car (in pounds). A sample of 50 recent car models was selected and the results recorded. (provided in auto.xlxs)

(a)  Using the sample data attached, calculate the sample mean and standard deviation for the variables: –

1. Miles per gallon (MPG)
2. Horsepower
3. Weight (in pounds)

(b)  Is there any evidence of skewness in the data sets? Which data set displays greatest skewness?

(c)  Using the sample data on MPG, calculate the sample proportion of vehicles whose fuel economy exceeds 37 mpg and its corresponding standard deviation.

(d)  Indicate all possible relationship between the variables and comment on it. (You may use scatter diagram or Karl Pearson’s correlation coefficient)

(e)  Using the complete data set and using simple ordinary least squares regression formula develop two models to explain the behavior of gasoline mileage (Miles per gallon) as a function of their-

(i) Horsepower

(ii) Weight

(f)  Which model best describes the behavior of gasoline mileage? Explain your reasons here.             10 MARKS

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Management

AUTO Data