Data Analysis Exam Prep
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Data Analysis Exam Prep
Sample questions with model answers
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6. (b) (The Reddy Mikks Company): Reddy Mikks produces both interior and exterior paints from two raw materials, M1 and M2. The following table provides the basic data of the problem: Exterior paint: Tons of raw material M1 per ton of paint: 6, Tons of raw material M2 per ton of paint: 1, Profit per ton ($1000): 5, Maximum daily availability: Raw material M1: 24 tons, Raw material M2: 6 tons. A market survey indicates that the daily demand for interior paint cannot exceed that for exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. Reddy Mikks wants to determine the optimum (best) product mix of interior and exterior paints that maximizes the total daily profit: Formulate the LPP and solve it with graphical method.
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Formulate the LPP and illustrate the solution graphically.
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1. (a) Draw the histogram of the above data. Find the value of mode (through histogram or otherwise).
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Draw a histogram and identify the mode from the data.
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1. (b) Calculate the mean and standard-deviation for the following distribution:
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Use the formulas for mean and standard deviation to calculate.
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3. (a) Twenty people were attacked by a disease and only 18 survived. Test the hypothesis that the survival rate, if attacked by this disease, is 85% or more at 5% level of significance.
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Perform a hypothesis test using the Z-test.
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4. (b) The demand for a particular spare part in a factory was found to vary day-to-day. In a sample study the following information was obtained: Days Mon. Tues. Wed. Thurs. Fri. Sat. No. of parts demanded 1124, 125, 110, 1120, 1126, 1115. Test the hypothesis that the number of parts demanded does not depend on the day of the week.
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Perform a Chi-square test for independence.
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5. (b) Using the above data: (i) Obtain the regression equation of sales on advertising.
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Derive the regression equation using least squares.
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7. (a) Find Initial basic feasible solution of the following transportation problem by Vogel's Approximation Method (VAM) and Least cost method.
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Apply VAM and Least Cost Method to find the solution.
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7. (b) A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the times that each man would take to perform each task is given in the matrix below: Tasks Subordinates I II III IV A 8 26 17 11 B 13 28 4 26 C 38 19 18 15 D 19 26 24 10. How should the tasks be allocated to subordinates so as to minimize the total man-hours?
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Use the assignment method to allocate tasks.
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2. (a) The numbers 1 2 3 4 5 and 6 are written on slips of paper and two of these slips are drawn. Determine the following probabilities: (i) One of the numbers drawn is odd or greater than 3?
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Calculate the probability based on combinations.
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2. (a) (ii) The numbers drawn are both even?
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Calculate the probability of drawing two even numbers.
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2. (b) Write short notes on any two of the following topics: (i) Integer Programming Problem (ii) Skewness and Kurtosis (iii) Application of LP in Operations Management (iv) Sample and Population
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Provide concise definitions and explanations for two selected topics.
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3. (b) A hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson distribution with mean 1.5. Calculate the proportion of days on which: (i) Neither car is used.
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Use the Poisson formula to find the probability.
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3. (b) (ii) Some demand is unfulfilled.
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Calculate the probability of unfulfilled demand.
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4. (a) X is a normal variate with mean 30 and S.D. 5: Find the probability that: (i) 26 ≤ X ≤ 40.
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Use the Z-score formula to calculate the probability.
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4. (a) (ii) X ≥ 45.
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Calculate the probability using Z-scores.
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4. (a) (iii) X ≤ 20.
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Use Z-scores to find the probability.
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5. (a) The following data relate monthly advertising spend (in lakh) and sales revenue (in crore): Calculate the coefficient of correlation.
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Use the correlation formula to calculate.
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6. (a) Write the dual of the LPP: Maximise z = 3x1 + 2x2 Subject to: x1 ≤ 4, x2 ≤ 6, x1 + x2 ≤ 5, x1, x2 ≥ 0.
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Formulate the dual linear programming problem.
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5. (a) (ii) Comment on the strength and direction of the relationship.
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Discuss based on the correlation coefficient.
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5. (b) (ii) Estimate sales revenue when advertising expenditure is ₹ 8 lakh.
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Substitute into the regression equation.
The full exam-length answer is in the app.
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