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Table of Contents
TU Exam Question 2072
Time: 3 hrs | Full Marks: 100 | Pass Marks: 35
Candidates are required to give their answer in their own words as far as practicable. The figures in the margin indicate full marks.
Attempt All Questions
Group A
Brief Questions Answer [10×2=20]
1. The average monthly salary of 10 male staffs and 5 female staffs of a manufacturing company are Rs.20,000 and Rs.18,000 respectively. Find the average monthly salary of all staffs taken together.
2. The mean and coefficient of variation of a certain data set are 12 and 25% respectively. Calculate the value of standard deviation and variance of the data.
3. What is the meaning of classification of data in statistics?
4. List the five number summary from the following daily sales data (in Rs.000) of seven different shops:
Sales (Rs.000) | 50 | 20 | 80 | 10 | 60 | 30 | 70 |
Shops | A | B | C | D | E | F | G |
5. Test for the normality of the distribution on the basis of the following information:
Lower quartile (Q_{1})=41.5, Upper quartile (Q_{1}=58.25
Ten^{th} percentile (P_{10})=31.428, 90^{th} percentile (P_{90})=70.
6. For eight pairs of observations on two variables sales (X) and pricing (Y), the following results were obtained.
∑X=156, ∑Y=132, ∑X²=4162, ∑Y²=2434, ∑XY=2844
Find out if there exists any relationship between sales and pricing.
7. Find the adjoint matrix of the matrix given below:
8. The probability that a manufacturer will produce ‘brand X’ product is 0.13, the probability that he will produce ‘brand Y’ product is 0.28 and the probability that he will produce both brands is 0.06. What is the probability that the manufacturer who has produced ‘brand Y’ will also have produced ‘brand X’?
9. Given that ∑PW=12610, ∑W=100, where P and W have their usual meaning. Calculate the cost of living index.
A man of middle class family of a remote area of Nepal was earning Rs.50,000 in the base period. What should be his salary in the current period, if his living standard is to remain the same?
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10. Consider the following straight line trend equation obtained from the data of annual profit (in Rs.000′)
Y=90+2X
Interpret the meaning of coefficient of ‘X’ of this model. What is monthly increase in profit?
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Group B
Descriptive Solution Questions
Attempt Five questions. [5×10=50]
11. The mean and variance of the marks in statistics obtained by all the 50 students of a certain college was computed as 60 and 100 respectively. Later on it was discovered that the scored 76 was wrongly taken as 67. Find the mean and standard deviation of scores when wrong value is omitted? Also calculate the coefficient of variation of marks after ignoring wrong value?
12. (a) Difference between “census” and “sampling” method of data collection. Why sampling method is suitable to collect data from large population?
(b) A Manufacturing Company Ltd. produces two types of drugs D_{1} and D_{2} with the help of three chemicals C_{1}, C_{2} and C_{3}.
The quantity of chemical requirements per kg of each D_{1} and D_{1} are given below in suitable units.
D_{1} | D_{2} | |
C_{1} | 10 | 12 |
C_{2} | 16 | 15 |
C_{3} | 8 | 16 |
The price of chemicals in three different markets M_{1}, M_{2} and M_{3} are as follows:
C_{1} | C_{2} | C_{3} | |
M_{1} | 20 | 19 | 16 |
M_{2} | 8 | 9 | 7 |
M_{3} | 6 | 7 | 8 |
Find the price per kg of each drug in each market by using matrix algebra.
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13. (a) The first four moments of a distribution about the arbitrary value 5 are 2, 30, 40 and 50. Calculate the mean, standard deviation, skewness and kurtosis of the distribution.
(b) Assuming that a factory has two machines M_{1} and M,sub>2. Past record showed that machine M_{1} produces 30% of the items of output and machine M2 produces 70% of the items. Further, 5% and 1% of the items produced by machine M_{1} and M_{2} respectively were defective. If a defective item is selected at random what is the probability that it was produced by machine M_{2}?
14. A frequency distribution of marks of 100 students is given below. Frequencies corresponding to two groups are missing from the table. The media is known to be 49.5 marks.
Marks | 0-19 | 20-39 | 40-59 | 60-79 | 80-99 |
No. of students | 14 | ? | 26 | ? | 16 |
i. Find the missing frequencies.
ii. Calculate the limits of marks obtained by middle 60% students.
15. By using properties of determinant, prove that
16. Calculate the index number by using suitable formula for 1983 on the basis of 1982 from the following information:
Article-I | Article-II | Article-III | ||||
Year | Price | Exp. | Price | Exp. | Price | Exp. |
1982 | 5 | 50 | 8 | 48 | 6 | 18 |
1983 | 4 | 48 | 7 | 49 | 5 | 20 |
Group C
Analytical solution questions
Attempt any Two questions [2×15=30]
17. Under an employment promotion programme, it is proposed to allow sale of newspapers on the buses during peak hours. A newspaper boy has the following probability of selling a magazine.
No. of copies sold | 10 | 11 | 12 | 13 | 14 |
Probability | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 |
Cost per copy of magazine and sale price per copy is Rs.50.
He cannot return unsold copies where salvage value is zero.
(a) Construct a pay-off table.
(b) Calculate the expected monetary value (EMV) for each strategy.
(c) How many copies should be ordered.
(d) Compute expected profit with perfect information (EPPI).
(e) Also calculate expected value of perfect information (EVPI) and interpret.
18. The following table represent the annual trend of net profit of two different companies seeking investment for their development project. In which company would you invest money, justify your solution by using necessary statistical tool.
Net profit in millions Rs. | ||
2001 | 16 | 16 |
2002 | 32 | 16 |
2003 | 40 | 22 |
2004 | 24 | 36 |
2005 | 40 | 40 |
2006 | 32 | 44 |
2007 | 88 | 48 |
19. The data in sales and promotion expenditures on a newly launched product for 6 years in given below:
Year | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 |
Sales (in Rs.00,000) | 16 | 20 | 18 | 24 | 20 | 22 |
Promotion expenses (Rs.’000) | 4 | 4 | 6 | 10 | 10 | 12 |
a. Calculate the two regression coefficients from the above data of sales and expenses.
b. Compute the correlation coefficient between sales and promotional expenditure and interpret.
c. Test the significance of the correlation coefficient.
d. Develop the estimating equation that describes the effect if promotional expenses in Rs.20,000.
e. Explain the meaning of each parameter of the equation; in terms of above information.
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