Data Analysis Exam Prep
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Data Analysis Exam Prep
Sample questions with model answers
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6. (b) Reddy Mikks produces both interior and exterior paints from two raw materials, M1 and M2. Formulate the LPP and solve it with graphical method.
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Set up the LPP and illustrate the graphical method.
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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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Use hypothesis testing procedures and Z-value.
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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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Use Chi-square test for independence.
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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.
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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.
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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 correlation formula to calculate.
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5. (b) Using the above data: (i) Obtain the regression equation of sales on advertising.
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Derive 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 solution.
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7. (b) A departmental head has four subordinates and four tasks to be performed. How should the tasks be allocated to subordinates so as to minimize the total man-hours?
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Use assignment problem techniques to minimize time.
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5. (b) (ii) Estimate sales revenue when advertising expenditure is 8 lakh.
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Substitute into regression equation.
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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 total outcomes.
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2. (a) (ii) The numbers drawn are both even?
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Calculate the probability of both numbers being even.
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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 or 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 Poisson probability formula.
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3. (b) (ii) Some demand is unfulfilled.
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Calculate using Poisson distribution properties.
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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 Z-scores to find the probability.
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4. (a) (ii) X ≥ 45.
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Calculate probability using Z-table.
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4. (a) (iii) X ≤ 20.
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Find probability using normal distribution.
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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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