STATISTICS AND BUSINESS MATHEMATICS B.com-1 Private Annual Examination 2015

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1 B.com-1 STATISTICS AND BUSINESS MATHEMATICS B.com-1 Private Annual Examination 2015 Compiled & Solved By: JAHANGEER KHAN

2 (SECTION A) Q.1 (a): Find the distance between the points (1, 2), (4, 5). SOLUTION (1-a): As we know that Substituting values: Q.1 (b): Find the roots of the function. SOLUTION (1-b): As we know that By substituting values pg. 1

3 Hence Solution Set = {, } Q.2 (a): Find the equation of straight line passing through the points (3, -2), (5, 1). SOLUTION (2-a): As we know that Substituting values: Q.2 (b): Find the derivative of the function (i); (ii) SOLUTION (2-b-i): pg. 2

4 SOLUTION (2-b-ii): Q.3 (a): Solve the equation by Cramer s rule:, SOLUTION (3-a): pg. 3

5 As we know that Substituting values: Hence Solution Set = {, } Q.3 (b): Given two matrices * +, * + Show that SOLUTION (3-b): * + * + [ ] * + * + * + * + pg. 4

6 * + * + * + * + [ ] * + * + * + * + (SECTION B) Q.4 (a): Fill in the blanks: (i) Statistics mainly concerned with data. (ii) Ogive is used to find. (iii) The standard deviation is positive square root of. (iv) The limit of coefficient of correlation is. (v) The base year index is always. SOLUTION (4-a): (i) Statistics mainly concerned with sample data. (ii) Ogive is used to find Median. (iii) The standard deviation is positive square root of Variance. (iv) The limit of coefficient of correlation is. (v) The base year index is always 100%. Q.4(b): Find Mean, mode and comments on the shape of distribution SOLUTION (4-b): Total pg. 5

7 Hence Solution Set = {, } Comment: Since Mean > Mode so, the distribution is skewed to the right Q.5(a): Calculate Mean absolute deviation about mean: 32, 28, 47, 63, 75, 39, 10, 60, 96 SOLUTION (5-a): pg. 6

8 Q.5(b): Find the variance of the numbers; 1, 2, 3, 4, 5. SOLUTION (5-b): Q.5(c): Find the coefficient of variation: SOLUTION (5-c): pg. 7

9 Q.6(a): Find Regression line y on x. X y SOLUTION (6-a): pg. 8

10 Q.6(b): Calculate Karl Pearson coefficient of correlation: x y SOLUTION (6-b): * +* + * +* + * +* + * +* + pg. 9

11 Q.6(c): Shift the base year from 1991 to 1995: Year Price Index % SOLUTION (6-c): (SECTION C) Q.7(a): Find the number of permutations of the words (i) KARIM (ii) ACCOUNTANT SOLUTION (7-a-i): n pg. 10

12 Compiled & Solved By: JAHANGEER KHAN SOLUTION (7-a-ii): n Q.7(b): From a group of 5 men and 3 women. How many combinations are possible with 2 men and 1 woman? SOLUTION (7-b): n ( ) 2 men and 1 woman from 5 men and 3 women can be selected into following ways: 5 x3 ( Q.7(c): ) ( ) Two unbiased coins are tossed once: Find the probability of (i) No head (ii) Two tails SOLUTION (7-c-i): pg. 11

13 * + * + SOLUTION (7-c-ii): * + * + Q.8(a): A random sample of 36 students selected from different colleges showed an average number of marks 62 with S.D of 5. Construct 95% confidence interval for the average marks of all students. SOLUTION (8-a): (95% Confidence Interval) 5 pg. 12

14 ( ) ( ) Q.8(b): A plant manufactures 8% of defective items. A sample of 6 is selected. What is the probability that: (i) At most two are defective (ii) all are defective. SOLUTION (8-b-i): n SOLUTION (8-b-i): pg. 13

15 n 6 Q.9(a): Draw all possible samples each of size 2 from population 9, 11, 15, 21. Show that E=µ. SOLUTION (9-a): If Repetition is not Allowed. E = µ S.no Samples Sample Mean 1. 9, , , , , , Total Verified If Repetition is Allowed. S.no Samples Sample Mean 1. 9, , , , , , , , , 9 12 pg. 14

16 E = µ Compiled & Solved By: JAHANGEER KHAN , , , , , , , Total Verified Q.9(b): A random variable follows Poisson Dist. With mean is 1.5 Find: (i) (ii) SOLUTION (9-b-i): SOLUTION (9-b-ii): pg. 15

17 Q.10(a): A random sample of size 16 was found to have and. Test the hypotheses against at SOLUTION (10-a): 1. H 0 : 2. H A : 3. α 1% OR Use test: 5. Critical Value: 6. Decision/Conclusion: Since > so reject H 0 and accept H A. it means that population mean is not equal to 32. Q.10(b): Given two random samples of size with and Test the Hypotheses against at. SOLUTION (10-b): pg. 16

18 1. H 0 : 2. H A : 3. α Use test: ( ) pg. 17

19 5. Critical Value: 6. Decision/Conclusion: Since > so reject H 0 and accept H A. it means that. pg. 18

STATISTICS AND BUSINESS MATHEMATICS B.com-1 Regular Annual Examination 2015

B.com-1 STATISTICS AND BUSINESS MATHEMATICS B.com-1 Regular Annual Examination 2015 Compiled & Solved By: JAHANGEER KHAN (SECTION A) Q.1 (a): Find the equation of straight line when x-intercept = 3 and