Available MS08 Quantitative Analysis for Managerial Applications previous year exam question answer for June 2022, Dec 2021 and June 2021. You can prepare previous exam paper answer for better performance.
June 2022
Q1. The daily cost, CD, of operating a hospital, is a linear function of the number of in-patients, IP, and out-patients, P, plus a fixed cost, a, i.e.,
CD = a + bP + dIP
Given the following data for three days, find the value of a, b and d by setting up a linear system of equations and using the matrix inverse
| Day | Cost (CD) (in INR) | No. of in-patients, IP | No. of out-patients, P |
| 1 | 6,950 | 40 | 10 |
| 2 | 6,725 | 35 | 9 |
| 3 | 7,100 | 40 | 12 |
Q2. Discuss the validity of the following statement: “A secondary source is not as reliable as a primary source.”
Q3. A highway petrol pump can serve on an average 15 cars per hour. What is the probability that for a particular car, the time taken will be less than 3 minutes? (The value of e–0·75 = 0·4724)
Q4. Why is forecasting so important in business? Identify applications of forecasting for medium-term decisions.
Q5. The number of automobile accidents per week that took place during peak traffic hours in a metropolis reported for 10 weeks were 12, 8, 20, 2, 14, 10, 15, 6, 9, 4. Are the frequencies in agreement with the belief that accident conditions were the same during this 10-week period?
(The value of test-statistic at = α = 0.05 and df = 9 is 16.92)
- Write short notes on any three of the following:
(a) Arithmetic Progression
(b) Census and Sample
(c) Bernoulli Process
(d) Systematic Sampling
(e) Linear Regression
Section B
Q7. In a university, 30 percent of the students doing a course in Statistics use the book authored by A1, 45 percent use the one authored by A2, and 25 percent use the one authored by A3. The proportion of students who learnt about each of these books through their teachers are: A1 = 0·50, A2 = 0·30 and A3 = 0·20. One of the students selected at random revealed that he learnt about the book he is using through his teachers. Find the probabilities that the book used is authored by A1, A2 and A3, respectively.
Q8. Calculate the correlation of the following data using Karl Pearson’s method
| Series A | Series B |
| 112 | 200 |
| 114 | 190 |
| 108 | 214 |
| 124 | 187 |
| 145 | 170 |
| 150 | 170 |
| 119 | 210 |
| 125 | 190 |
| 147 | 180 |
| 150 | 181 |
Dec 2021
Q1. “A model is the representation of a system which, in turn, represents a specific part of reality.” Explain models for Quantitative Analysis in the light of the statement. Also explain the various types of models.
Q2. Distinguish between Karl Pearson’s and Bowley’s coefficient of skewness. Which one of these would you prefer and why?
Q3. The distribution of the total time a light bulb will burn from the moment it is first put into service is known to be exponential with mean time between failure of the bulbs equal to 1000 hours. What is the probability that a bulb will burn more than 1000 hours? (The value of e = 2·7182)
Q4. In a locality, where, out of the 5000 people residing, 1200 are above 30 years of age and 3000 are female. Out of the 1200, who are above 30 years of age, 200 are females. Suppose, a person is chosen at random and found to be a female, what is the probability that she is above 30 years of age?
Q5. The ranks obtained by a set of ten students in a Mathematics test (Variable X) and a Physics test (Variable Y) are shown below:
| Rank for Variable X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Rank for Variable Y | 3 | 1 | 4 | 2 | 6 | 9 | 8 | 10 | 5 | 7 |
Determine the rank correlation.
Q6. Write short notes on any three of the following :
(a) Geometric Progression
(b) Questionnaire
(c) Poisson Distribution
(d) Stratified Sampling
(e) Time Series Analysis
Section B
Q7. A production engineer finds that, on an average, mechanics working in a machine shop complete a certain task in 15 minutes. The time required to complete the task is approximately normally distributed with a standard deviation of 3 minutes. Find the probabilities that the task is completed (a) in less than 8 minutes, and (b) in more than 9 minutes.
(Area under the standard normal curve from 0 to z = 0·4901 (for part a), and area under the standard normal curve from 0 to z = 0·4772 (for part b)
Q8. A cricket team expected the chances of its winning a game as 75 percent. Out of 80 games played during the course of the year, 55 games are won and 25 are lost. Are the observed data consistent with the expectation of the team? Use α = 0.05. (The test statistic at 0.05 is 3:84).
June 2021
Q1. Solve the following system of linear equations, using matrix method or any other method that you prefer:
2x + 3y + 3z = 5
x – 2y + z = – 4
3x – y – 2z = 3
Q2. What do you understand by the terms Primary data and Secondary data? Explain some of the points to be kept in mind while designing a questionnaire.
Q3. What do you mean by Probability? What are the different approaches to Probability theory? Explain it with the help of an example.
Q4. A marketing research firm wants to estimate the share that foreign companies have in the Indian market for certain products. A random sample of 100 consumers is obtained, and it is found that 34 people in the sample are the users of foreign-made products; the rest are users of domestic products. Give a 95% confidence interval for the share of foreign products in this market.
(The value of test statistic at 95% confidence level is 126)
Q5. What do you mean by Time Series Analysis ? How would you conduct such an analysis for forecasting the sales of a product in your firm?
- Write short notes on any three of the following :
(a) Conditions of Maxima and Minima
(b) Mathematical Properties of Median
(c) Exponential Distribution
(d) Stratified Sampling
(e) Least Square Criterion
Section B
Q7. An aircraft manufacturer is concerned about variability in the diameters of lids used to seal fuel tanks. Only a narrow range of diameters is acceptable. A sample of 20 fuel-tank lids is taken. After measuring the 20 diameters, an engineer finds them to have a standard deviation of 0.095 inches. Conduct a test at 2% level of significance to see whether population variation of lid diameters equals 0.0001 inches squared, as specified by engineers.
(The value of test statistic at α= 0.01, 19 degrees of freedom is 36.91)
(The value of test statistic at α= 0.99 is 7.633 at 19 degrees of freedom)
Q8. Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all the students who reside in hostel attain A-grade in their annual examination and 20% of day scholars attain A-grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A-grade. What is the probability that the student is a hosteler?
